03-visualization.utf8

# 统计学原理(Statistic)

### 胡华平

### 西北农林科技大学

### 经济管理学院数量经济教研室

### huhuaping01@hotmail.com

### 2021-05-08

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---
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# 第三章 数据的图表展示

### [3.1 数据的预处理](#prepare)

### [3.2 品质数据的整理与显示](#quality)

### [3.3 数值型数据的整理与显示](#quantity)

### [3.4 合理使用图表](#nice)

---
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# 3.1 数据的预处理

### 数据清洗（data cleaning ）

### 数据变换（data transformation）

### 数据子集(data subset)

---
layout: true

<div class="my-footer"><span>huhuaping@  &emsp;&emsp; <a href="#chapter02"> 第03章 数据的图表展示 </a>
&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;
<a href="#prepare"> 3.1 数据的预处理 </a> </span></div>

---

## 数据预处理的主要内容

- 数据审核：检查数据中的错误

- 数据筛选：找出符合条件的数据

- 数据排序：升序和降序；寻找数据的基本特征

- 数据透视：按需要汇总

---

## 数据预处理：数据审核

对于**原始数据(raw data)**需要进行：

**完整性审核**：

- 应调查的单位或个体是否有遗漏

- 所有的调查项目或变量是否填写齐全

**准确性审核**：

- 数据是否真实反映实际情况，内容是否符合实际

- 数据是否有错误，计算是否正确等

---

## 数据预处理：数据审核

对于**二手数据(second hand data)**需要进行：

**适用性审核**：

- 弄清楚数据的来源、数据的口径以及有关的背景材料

- 确定数据是否符合自己分析研究的需要

**时效性审核**：

- 尽可能使用最新的数据

- 确认是否有必要做进一步的加工整理

---

## 数据预处理：数据筛选

**数据预处理**：当数据中的错误不能予以纠正，或者有些数据不符合调查的要求而又无法弥补时，需要对数据进行筛选。

数据筛选的内容：

- 将某些不符合要求的数据或有明显错误的数据予以剔除

- 将符合某种特定条件的数据筛选出来，而不符合特定条件的数据予以剔除

---

## 数据预处理：数据排序

数据排序的**作用**：

- 按一定顺序将数据排列，以发现一些明显的特征或趋势，找到解决问题的线索

- 排序有助于对数据检查纠错，以及为重新归类或分组等提供依据

- 在某些场合，排序本身就是分析的目的之一

- 排序可借助于计算机完成

---

## 数据预处理：数据透视表

数据透视表（pivot table）的作用：

- 可以从复杂的数据中提取有用的信息

- 可以对数据表的重要信息按使用者的习惯或分析要求进行汇总和作图

- 形成一个符合需要的交叉表(列联表)

- 在利用数据透视表时，数据源表中的首行必须有列标题

---

## 数据预处理：Excel中的数据透视表

利用`Excel`软件创建数据透视表的主要步骤：

- 第1步：在Excel工作表中建立数据清单

- 第2步：选中数据清单中的任意单元格，并选择【数据】菜单中的【数据透视表和数据透视图】

- 第3步：确定数据源区域

- 第4步：在【向导—3步骤之3】中选择数据透视表的输出位置。然后选择【布局】

- 第5步：在【向导—布局】对话框中，依次将”分类变量“拖至左边的“行”区域，上边的“列”区域，将需要汇总的“变量” 拖至“数据区域”

- 第6步：然后单击【确定】，自动返回【向导—3步骤之3】对话框。然后单击【完成】，即可输出数据透视表

---

### （演示）Excel数据预处理：数据准备

利用Excel进行数据准备，主要工作包括：

- 读取或导入其他数据格式（例如`.txt`或`.csv`格式）

- 删除说明性内容

- 数据表形式（long data VS wide data）

- 数值表达方式（labels VS values）

- 备注重要信息

---

### （演示）导入其他数据格式：Excel操作

]

]

]

---

### （演示）删除说明性内容：Excel操作

]

---

### （演示）删除说明性内容：Excel操作

#### b.删除后
]

]

---
exclude: true

### （演示）删除说明性内容：Excel操作

]

]

---

### （演示）数据表现形式：Excel操作

- 一个病人的数据，由一行就能够完全进行表达。

]

---

### （演示）数据表现形式：Excel操作

### 2)窄长形式
]

- 一个病人的数据，需要多行才能进行完整表达。

]

---
exclude: true

### （演示）数据表现形式：Excel操作

> 一个病人的数据，由一行就能够完全进行表达。

]

> 一个病人的数据，需要多行才能进行完整表达。

]

---

## 数据清洗：Excel常用操作1

- **查找/替换**：

- **提取文本字符**：

- 从左侧：`=LEFT(text, [num_chars])`
    - 从右侧：`=RIGHT(text, [num_chars])`
    - 从指定位置：`=MID(text,start_num,num_chars)`

- **正确大小写**：

- 全部小写：`=LOWER(text)`
    - 全部大写：`=UPPER(text)`
    - 首字母大写：`=PROPER(text)`
    - 自定义大小写：`=UPPER(LEFT(A2,1)&LOWER(MID(A2,2,60)`
    
---

## 数据清洗：Excel常用操作2

- **删除重复值**：

- **合并文本内容**：`=[Cell 1]&[Cell 2]`

- **清除空格**：`=TRIM( text )`

- **清除非打印字符**：`=CLEAN( text )`

---

### （演示）Excel数据清洗：查找/替换

---

### （演示）Excel数据清洗：提取文本字符

---

## （演示）Excel数据清洗：自定义大小写

---

### （演示）Excel数据清洗：删除重复值

---

### （演示）Excel数据审核：

]

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---

### 数据清洗：清单

以**调查问卷数据**的清洗为例：

- 真实性的清洗：要确认数据来自于受访者。

- 完整性的清洗：主要看样本无应答，也就是一整份问卷没有应答。以及选项无应答，也就是应该应答的访题没有应答。

- 可用性的清洗：主要是看编码是否完成，权数是否可行，以及缺失值如何标记和处理。

- 错误性的清洗：主要是清洗调查环节的错误，比如样本错误、应答人错误、应答方式错误。

---
exclude: true

### 案例：家庭税收情况

---

### 案例：家庭税收情况

**案例说明**：一项家庭税收情况调查，一共收集了样本数
`$n=73262$`个家庭在13个变量上的基本情况。

```
Rows: 73,262
Columns: 13
$ id             <int> 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13,...
$ custid         <chr> "000006646_03", "000007827_01", "000008359...
$ sex            <fct> Male, Female, Female, Female, Male, Male, ...
$ is_employed    <lgl> TRUE, NA, TRUE, NA, TRUE, NA, TRUE, NA, TR...
$ income         <dbl> 22000, 23200, 21000, 37770, 39000, 11100, ...
$ marital_status <fct> Never married, Divorced/Separated, Never m...
$ health_ins     <lgl> TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, FALSE,...
$ housing_type   <fct> Homeowner free and clear, Rented, Homeowne...
$ recent_move    <lgl> FALSE, TRUE, FALSE, FALSE, FALSE, FALSE, F...
$ num_vehicles   <dbl> 0, 0, 2, 1, 2, 2, 2, 2, 5, 3, 2, 2, 5, 1, ...
$ age            <dbl> 24, 82, 31, 93, 67, 76, 26, 73, 27, 54, 61...
$ state_of_res   <fct> Alabama, Alabama, Alabama, Alabama, Alabam...
$ gas_usage      <dbl> 210, 3, 40, 120, 3, 200, 3, 50, 3, 20, 3, ...
```

]

---

### （税收案例）变量视图

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---

### （税收案例）数据视图

数据包含的样本数
`$n=73262$`，下表展示了前500行。

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---

### （税收案例）数据清洗问题——存在混合编码

`gas_usage`变量表示用油支出，样本数据中的分布情况如下：

```

1     2     3     4    10    20    30    40    50    60    70 
 2389  6609 24984   455  1376  4163  5149  4242  4118  2585  1909 
   80    90   100   110   120   130   140   150   160   170   180 
 2330  1331  2651   636   836   700   446  1049   299   238   331 
  190   200   210   220   230   240   250   260   270   280   290 
  175   823   113    88   111    89   256    54    40    61    33 
  300   310   320   330   340   350   360   370   380   390   400 
  255    13    26    20    36    53     5    39    19     9    79 
  410   420   430   440   450   460   470   480   490   510   520 
   37    15     1     3    48    43    39    72    35     3     3 
  540   570  <NA> 
    9    11  1720 
```

]

根据“数据集说明”，我们容易发现`gas_usage`变量数据存在混合编码问题：

- 混合了数值（number）和字符（string）：
    - 1表示包含在电子支付中；2表示包含在出租或分户中；3表示没有用油；
    - 004-999表示用油支出数（美元）。

- 有缺失值：
    - `NA`表示缺失。

]

我们需要把原来的变量`gass_usage`提取构建为4个新变量：`gas_usage_new`、`gas_with_rent`、 `gas_with_electricity`、`no_gas_bill`。

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]

---

### （税收案例）数据清洗问题——数据范围失常

我们容易发现，年龄变量`age`存在取值为0，或大于100的情形。

```

0   21   22   23   24   25   26   27   28   29   30   31   32   33 
  77 1365 1312 1348 1302 1424 1489 1407 1364 1284 1444 1303 1351 1327 
  34   35   36   37   38   39   40   41   42   43   44   45   46   47 
1285 1367 1284 1216 1226 1190 1327 1202 1215 1203 1262 1449 1392 1217 
  48   49   50   51   52   53   54   55   56   57   58   59   60   61 
1244 1197 1355 1352 1349 1397 1429 1292 1392 1326 1290 1307 1333 1281 
  62   63   64   65   66   67   68   69   70   71   72   73   74   75 
1220 1175 1124 1113 1082 1062  999 1026  792  696  800  757  645  549 
  76   77   78   79   80   81   82   83   84   85   86   87   88   89 
 519  530  517  431  419  424  358  314  301  317  267  251  202  162 
  90   91   92   93   94   95   96  100  110  114  120 <NA> 
 130   57   83  124  277   91    6   72   66   62   66    0 
```

]

此外，我们还发现收入变量`income`存在取值小于0的情形。

```

-6900   -6800   -6700   -6600   -6100   -6000   -5900   -5800 
      1       2       2       1       1       5       1       1 
  -5700   -5500   -5400   -5300   -5200   -5000   -4900   -4700 
      1       2       2       1       2       2       1       2 
  -4520   -4500   -4200   -3500   -3100   -2800   -2700   -2400 
      1       2       1       1       1       1       1       1 
  -1800   -1700   -1500    -800    -700    -630    -400    -160 
      1       1       2       1       1       1       1       1 
      0       1       4      10      20      30      40      50 
   6811      18      18       8      10      16       4      10 
     60      70      80      90     100     110     120     130 
     10       6       7       3      39       4       9       6 
    140     150     160     170     180     190     200     210 
      7       8       4       5       3       5      56       3 
    220     230     240     250     260     270     280     300 
      5       2      10      14       1       3       1      49 
    310     320     330     340     350     360     370     380 
      1       5       2       1      10      11       3       5 
    400     410     420     430     440     450     460     470 
     33       1       3       3       1       9       4       2 
    480     500     510     520     530     540     550     560 
      6      66       8       4       4       7       2       3 
    570     580     590     600     610     620     630     640 
      4       3       3      55       5       2       8       2 
    650     660     670     700     710     720     730     740 
      7       5      10      22       6       3       5       3 
    750     760     770     780     790     800     810     820 
     12       2       2       4       2      42       3       2 
    830     840     850     860     870     880     890     900 
     10       5       5       4       3       4       7      33 
    910     920     930     940     950     960     970     980 
      1       5       2       4       6       8       3       3 
    990    1000    1001    1050    1060    1100    1104    1150 
      3     161       1       1       1      29       1       2 
   1180    1190    1200    1250    1280    1300    1310    1320 
      1       1     127       2       3      83       1       1 
   1400    1450    1500    1504    1520    1570    1580    1600 
     82       1     118       1       2       1       1      73 
   1601    1620    1630    1680    1700    1710    1720    1750 
      1       1       1       1      43       1       1       1 
   1780    1800    1820    1830    1840    1850    1880    1900 
      1      78       1       1       2       1       1      36 
   1904    1980    2000    2020    2030    2040    2100    2110 
      1       1     244       1       2       3      39       1 
   2150    2160    2170    2180    2200    2220    2230    2240 
      1       1       1       1      66       1       2       2 
   2300    2350    2360    2390    2400    2404    2410    2430 
     56       1       1       1      93       1       1       1 
   2450    2460    2480    2500    2530    2550    2560    2590 
      2       1       2     101       1       1       1       1 
   2600    2690    2700    2730    2740    2750    2770    2790 
     38       1      45       1       1       1       1       1 
   2800    2840    2850    2890    2900    2910    2980    3000 
     36       1       1       1      24       1       1     259 
   3010    3060    3090    3100    3170    3180    3200    3201 
      1       2       1      27       1       2      54       2 
   3210    3230    3280    3300    3310    3320    3330    3400 
      1       1       1      45       1       1       1      37 
   3430    3500    3501    3520    3530    3540    3560    3600 
      2      88       2       1       1       1       1     111 
   3601    3604    3630    3650    3700    3730    3800    3804 
      1       1       3       1      20       1      47       1 
   3850    3880    3900    3950    3980    4000    4010    4050 
      2       1      28       1       1     252       1       1 
   4100    4180    4190    4200    4280    4300    4320    4350 
     23       1       1      55       1      45       1       1 
   4400    4420    4430    4500    4550    4580    4600    4620 
     27       1       1      74       1       1      33       1 
   4690    4700    4710    4750    4780    4800    4801    4810 
      1      40       1       1       1     134       1       1 
   4820    4840    4890    4900    4960    5000    5001    5010 
      1       1       1      32       2     430       3       1 
   5030    5050    5070    5080    5100    5130    5150    5190 
      1       4       1       1      33       1       2       1 
   5200    5210    5300    5340    5400    5500    5510    5540 
     58       2      38       2      62      76       4       1 
   5560    5570    5600    5640    5670    5690    5700    5720 
      1       1      47       2       1       1      37       2 
   5740    5760    5780    5800    5810    5830    5880    5900 
      1       2       1      56       2       1       1      33 
   5970    6000    6004    6010    6020    6050    6070    6100 
      1     436       1       2       1       3       1      33 
   6120    6130    6140    6150    6190    6200    6210    6230 
      2       1       1       1       1      36       1       1 
   6240    6250    6300    6360    6400    6410    6440    6500 
      1       1      42       1      45       1       1      89 
   6520    6550    6560    6580    6600    6640    6650    6660 
      1       1       1       1      74       1       1       1 
   6680    6700    6704    6750    6760    6790    6800    6880 
      1      63       1       2       1       1      41       1 
   6900    6950    6960    7000    7004    7010    7020    7030 
     45       1       1     301       1       2       1       3 
   7040    7060    7080    7100    7110    7140    7150    7190 
      1       1       1      32       1       2       1       1 
   7200    7220    7230    7240    7250    7260    7270    7300 
    226       1       2       2       1       1       1      49 
   7320    7340    7400    7420    7440    7450    7460    7470 
      1       1      48       1       1       1       1       1 
   7480    7500    7504    7550    7560    7600    7650    7660 
      1     126       1       1       2      58       2       1 
   7680    7700    7710    7740    7750    7760    7800    7801 
      1      45       1       1       1       3     100       1 
   7850    7860    7880    7900    7901    7920    7940    7980 
      1       1       1      51       1       1       1       1 
   8000    8001    8004    8030    8040    8050    8070    8100 
    476       2       1       1       2       3       1      52 
   8110    8120    8130    8140    8200    8230    8250    8280 
      1       1       2       1      51       1       1       2 
   8300    8304    8310    8350    8360    8400    8404    8450 
     64       1       1       1       2     273       2       2 
   8460    8470    8500    8510    8520    8540    8550    8560 
      3       1     106       1       2       1       1       2 
   8590    8600    8630    8640    8650    8680    8690    8700 
      1      92       1       1       2       3       2      78 
   8710    8750    8760    8800    8820    8860    8880    8900 
      3       1       1     353       2       1       1      89 
   8904    8940    8950    8970    8980    8990    8994    9000 
      1       2       1       3       1       2       1     453 
   9004    9010    9020    9030    9040    9050    9060    9070 
      1       2       2       3       3       2       2       1 
   9080    9100    9110    9150    9160    9180    9190    9200 
      1      81       3       1       2       1       1      66 
   9220    9240    9250    9270    9280    9290    9300    9310 
      2       2       2       1       1       4      64       2 
   9340    9350    9370    9390    9400    9420    9450    9460 
      2       3       1       2      74       1       1       3 
   9500    9520    9530    9550    9570    9600    9601    9604 
    108       1       1       2       1     271       2       1 
   9610    9620    9630    9640    9650    9660    9670    9680 
      1       1       1       2       1       1       1       1 
   9690    9700    9701    9710    9750    9760    9770    9780 
      3      62       1       1       3       1       1       2 
   9790    9800    9810    9840    9860    9870    9880    9900 
      2      99       2       1       1       1       1      58 
   9904    9910    9940    9950    9980   10000   10001   10004 
      1       1       1       1       2     855       1       2 
  10010   10011   10020   10030   10050   10060   10070   10100 
      2       1       2       3       1       1       1      64 
  10110   10130   10150   10190   10200   10201   10210   10220 
      1       1       3       1      87       1       2       1 
  10240   10250   10280   10290   10300   10304   10310   10380 
      3       5       1       1      67       1       1       1 
  10390   10400   10404   10410   10420   10430   10440   10450 
      1      90       1       1       1       3       2       3 
  10490   10500   10510   10530   10540   10550   10570   10590 
      1      99       1       1       1       2       1       1 
  10600   10601   10610   10650   10670   10690   10700   10710 
     53       2       1       1       1       1      82       2 
  10720   10730   10740   10750   10760   10800   10810   10820 
      1       1       2       1       1     182       1       2 
  10830   10850   10860   10900   10910   10940   10950   10990 
      1       2       1      66       1       1       1       1 
  11000   11004   11020   11040   11060   11070   11090   11100 
    291       1       1       3       1       1       1      58 
  11120   11150   11160   11170   11200   11204   11210   11240 
      1       1       2       2      77       1       1       1 
  11280   11300   11330   11350   11370   11390   11400   11430 
      1      67       1       1       1       1      79       1 
  11440   11450   11500   11501   11510   11530   11560   11600 
      1       2      90       1       1       1       1      55 
  11601   11620   11650   11690   11700   11730   11790   11800 
      1       1       2       1      56       2       3      62 
  11820   11900   11904   11920   11940   11950   12000   12001 
      1      56       1       1       1       2    1140       3 
  12004   12010   12020   12040   12050   12080   12100   12150 
      2       4       4       2       2       1      58       2 
  12160   12200   12210   12220   12240   12250   12280   12290 
      1      63       1       3       1       1       1       1 
  12300   12330   12350   12400   12401   12450   12460   12480 
     57       2       1      57       1       1       1       2 
  12500   12501   12504   12520   12530   12540   12550   12590 
    127       1       1       1       2       1       2       1 
  12600   12620   12630   12690   12700   12730   12760   12780 
     82       1       1       1      35       1       1       2 
  12800   12830   12850   12900   12910   12930   12940   12950 
     59       1       1      40       1       1       1       2 
  12960   12980   13000   13004   13020   13040   13050   13060 
      1       1     400       2       3       1       2       1 
  13100   13101   13120   13130   13140   13160   13190   13200 
     48       1       1       1       1       1       1     140 
  13204   13210   13230   13240   13250   13280   13300   13310 
      3       1       1       1       1       1      77       3 
  13340   13360   13380   13400   13420   13430   13440   13450 
      1       2       2      54       1       1       1       1 
  13500   13560   13600   13650   13670   13690   13700   13701 
     89       2      63       3       1       1      55       1 
  13720   13730   13750   13780   13790   13800   13830   13900 
      1       1       1       1       1      58       1      42 
  13901   13904   13910   13940   13950   13960   13980   14000 
      1       1       1       1       1       2       3     435 
  14004   14020   14030   14050   14070   14100   14120   14150 
      1       2       1       1       2      47       1       2 
  14160   14170   14180   14200   14201   14210   14230   14250 
      1       1       2      57       1       1       1       2 
  14280   14290   14300   14310   14350   14370   14390   14400 
      1       1      48       1       4       1       1     252 
  14410   14430   14440   14460   14490   14500   14501   14540 
      2       1       1       1       1      81       1       1 
  14580   14590   14600   14610   14620   14630   14650   14660 
      1       1      50       2       2       1       1       1 
  14670   14680   14700   14740   14800   14840   14850   14900 
      1       1      60       1      53       1       1      50 
  14910   14920   14930   14950   14960   15000   15001   15004 
      1       2       1       1       1     856       1       1 
  15010   15020   15030   15040   15050   15060   15090   15100 
      1       3       2       1       2       1       1      37 
  15120   15130   15140   15150   15200   15210   15220   15230 
      1       1       1       1      52       1       1       1 
  15260   15300   15301   15310   15320   15330   15350   15390 
      1      41       1       1       1       1       3       1 
  15400   15410   15420   15440   15450   15460   15480   15500 
     51       1       1       2       1       1       1      60 
  15501   15510   15520   15530   15540   15550   15580   15600 
      1       1       2       2       2       1       3     187 
  15601   15650   15700   15704   15750   15790   15800   15830 
      1       4      35       1       1       1      46       1 
  15840   15850   15890   15900   15920   15930   15940   15950 
      1       1       1      38       2       2       1       2 
  16000   16001   16020   16100   16120   16140   16190   16200 
    435       1       5      42       1       3       1      66 
  16240   16260   16270   16300   16304   16320   16330   16340 
      1       1       1      48       1       1       2       1 
  16350   16400   16430   16460   16500   16520   16530   16550 
      2      38       2       1      72       2       1       1 
  16560   16600   16620   16650   16670   16690   16700   16704 
      1      68       1       1       1       1      46       1 
  16720   16730   16790   16800   16810   16830   16850   16880 
      1       1       1     151       1       1       1       1 
  16900   16901   16930   16990   17000   17001   17004   17020 
     44       2       2       1     332       1       1       1 
  17040   17050   17070   17100   17150   17160   17180   17200 
      1       1       1      53       2       1       1      48 
  17230   17240   17250   17260   17300   17320   17330   17360 
      1       1       3       2      51       1       1       1 
  17400   17450   17460   17500   17501   17504   17520   17550 
     55       2       1      76       1       1       1       1 
  17590   17600   17610   17650   17700   17720   17730   17740 
      1      51       1       2      31       2       1       1 
  17760   17780   17790   17800   17830   17900   17904   17950 
      1       1       1      47       2      37       1       1 
  17980   18000   18010   18020   18040   18050   18080   18090 
      1     718       1       3       1       2       1       1 
  18100   18110   18120   18130   18140   18150   18200   18201 
     29       1       2       2       1       1      63       1 
  18230   18250   18300   18304   18310   18360   18400   18430 
      1       1      44       1       1       2      56       1 
  18480   18490   18500   18510   18520   18530   18560   18600 
      3       1      70       2       1       1       1      52 
  18610   18680   18700   18710   18780   18800   18810   18820 
      1       2      59       1       2      42       1       1 
  18830   18880   18890   18900   18920   18970   18990   19000 
      1       1       1      33       3       1       1     291 
  19010   19030   19080   19100   19104   19120   19200   19201 
      3       1       1      44       1       1     149       2 
  19210   19230   19250   19260   19290   19300   19350   19360 
      2       1       2       1       1      53       1       2 
  19400   19410   19430   19500   19504   19510   19520   19550 
     44       1       2      72       1       1       2       1 
  19560   19590   19600   19610   19620   19640   19650   19700 
      1       1      50       1       1       1       1      32 
  19720   19800   19801   19900   19920   19940   19990   20000 
      1      65       1      34       1       1       1    1411 
  20001   20004   20020   20030   20040   20050   20080   20100 
      1       4       1       1       1       3       1      53 
  20140   20150   20160   20180   20200   20230   20240   20300 
      2       1       2       1      41       1       1      43 
  20304   20310   20350   20370   20380   20390   20400   20410 
      1       1       1       1       2       1      79       1 
  20420   20440   20470   20480   20490   20500   20530   20600 
      2       1       1       1       1      38       1      64 
  20630   20640   20680   20700   20750   20800   20820   20860 
      1       1       1      37       1      96       1       1 
  20870   20880   20900   20950   21000   21001   21004   21010 
      1       1      33       1     327       1       1       2 
  21020   21030   21060   21080   21100   21110   21140   21200 
      3       4       1       1      31       1       1      37 
  21210   21230   21240   21250   21300   21320   21340   21350 
      2       1       1       1      45       1       1       2 
  21360   21400   21404   21420   21450   21460   21500   21590 
      1      26       1       1       3       1      56       1 
  21600   21604   21610   21620   21630   21640   21650   21700 
     91       1       2       1       2       1       1      25 
  21750   21800   21820   21840   21850   21860   21900   21901 
      1      45       1       2       1       1      35       1 
  21930   21940   22000   22010   22050   22090   22100   22120 
      1       1     484       2       2       1      38       1 
  22130   22150   22200   22240   22280   22300   22330   22350 
      1       2      55       1       2      31       1       2 
  22400   22430   22450   22500   22540   22550   22580   22590 
     43       1       1      79       1       2       1       1 
  22600   22610   22680   22700   22720   22730   22750   22800 
     28       1       1      28       1       1       2      54 
  22810   22830   22840   22850   22860   22880   22890   22900 
      1       1       3       1       1       1       1      51 
  22920   22950   22960   22970   22980   23000   23010   23040 
      1       1       1       1       1     354       1       1 
  23050   23100   23120   23130   23180   23190   23200   23250 
      2      28       1       1       1       1      51       1 
  23300   23301   23350   23360   23400   23480   23500   23501 
     36       1       2       1      56       1      46       1 
  23530   23600   23640   23680   23700   23740   23760   23790 
      2      30       1       1      32       1       2       1 
  23800   23820   23870   23900   23910   23950   23960   24000 
     54       1       1      25       2       1       1     789 
  24001   24004   24010   24020   24050   24070   24100   24101 
      5       3       1       3       4       1      27       1 
  24110   24130   24150   24160   24170   24200   24201   24300 
      1       1       2       1       1      31       1      28 
  24301   24304   24310   24360   24380   24390   24400   24410 
      1       1       1       1       1       1      38       1 
  24470   24500   24510   24530   24570   24580   24590   24600 
      1      51       1       1       1       1       1      48 
  24604   24700   24720   24760   24800   24810   24830   24840 
      1      39       2       2      29       1       1       1 
  24870   24880   24900   24920   24940   24950   24990   25000 
      1       1      25       2       1       1       1    1109 
  25001   25004   25010   25020   25040   25080   25100   25110 
      4       1       1       2       2       2      39       1 
  25130   25140   25150   25180   25200   25220   25230   25240 
      1       1       1       1      59       1       2       3 
  25250   25300   25330   25400   25410   25450   25460   25470 
      1      28       2      39       1       2       1       1 
  25480   25490   25500   25501   25530   25550   25590   25600 
      1       1      45       1       1       1       1      44 
  25604   25620   25700   25740   25750   25800   25810   25900 
      1       1      34       1       2      39       1      35 
  25930   25950   25960   26000   26001   26004   26010   26020 
      1       1       1     406       1       1       1       1 
  26030   26040   26060   26090   26100   26110   26120   26130 
      2       1       3       1      25       1       2       1 
  26150   26200   26220   26230   26250   26300   26310   26350 
      2      49       2       1       1      40       1       1 
  26380   26390   26400   26401   26420   26430   26450   26470 
      1       1      79       1       1       1       2       1 
  26480   26500   26530   26540   26570   26580   26600   26650 
      3      47       1       1       2       2      22       1 
  26700   26800   26850   26860   26900   26920   26930   26940 
     25      23       1       1      32       2       1       1 
  26990   27000   27004   27030   27050   27070   27100   27150 
      1     353       1       2       1       1      22       1 
  27200   27201   27250   27281   27300   27340   27360   27390 
     30       1       1       1      26       1       1       1 
  27400   27450   27480   27490   27500   27550   27600   27620 
     42       2       2       1      41       1      62       2 
  27630   27700   27720   27740   27750   27800   27860   27870 
      1      27       1       1       2      27       1       1 
  27884   27890   27900   27910   27920   27970   27980   27990 
      1       1      25       1       1       1       1       1 
  28000   28001   28004   28010   28020   28030   28040   28050 
    484       2       1       2       1       1       2       3 
  28090   28100   28120   28130   28170   28200   28300   28301 
      1      36       1       1       1      30      34       1 
  28304   28310   28350   28400   28401   28450   28470   28500 
      1       1       1      20       1       1       1      48 
  28504   28530   28540   28580   28600   28601   28660   28680 
      1       1       1       1      54       1       1       1 
  28700   28750   28800   28870   28900   28904   28930   28940 
     22       1      68       1      25       1       1       2 
  28950   29000   29040   29050   29060   29080   29100   29150 
      1     235       3       1       1       1      31       1 
  29190   29200   29210   29220   29230   29260   29280   29300 
      1      24       1       1       1       1       1      28 
  29350   29400   29430   29500   29520   29530   29550   29600 
      1      31       1      45       1       1       2      25 
  29650   29700   29701   29730   29780   29800   29810   29820 
      1      22       1       1       1      41       2       1 
  29900   29960   29970   30000   30001   30004   30010   30020 
     22       2       1    1672       3       3       2       5 
  30030   30040   30050   30060   30080   30100   30140   30150 
      3       3       3       1       1      27       1       2 
  30200   30240   30270   30280   30300   30320   30330   30350 
     33       1       1       1      30       1       1       1 
  30400   30430   30470   30500   30510   30520   30530   30540 
     31       2       1      39       1       1       2       1 
  30600   30601   30700   30710   30750   30800   30804   30850 
     32       1      27       1       1      28       1       1 
  30860   30900   30910   30940   31000   31001   31030   31050 
      1      26       1       1     214       1       1       1 
  31100   31110   31200   31210   31220   31300   31400   31430 
     22       2      85       1       1      18      23       1 
  31450   31460   31500   31520   31600   31650   31700   31720 
      2       1      36       2      34       1      24       1 
  31780   31800   31900   31904   32000   32001   32004   32010 
      1      34      14       1     607       1       2       1 
  32020   32030   32050   32090   32100   32150   32180   32200 
      1       1       2       1      16       2       1      39 
  32240   32250   32300   32320   32330   32400   32404   32420 
      1       1      22       1       1      61       1       2 
  32500   32520   32540   32570   32600   32610   32650   32700 
     39       1       1       1      32       2       2      14 
  32710   32780   32800   32830   32890   32900   33000   33001 
      1       1      24       1       1      17     259       2 
  33004   33010   33090   33100   33110   33140   33170   33200 
      1       1       1      23       1       1       1      24 
  33204   33280   33300   33400   33480   33490   33500   33510 
      1       1      43      29       1       1      28       1 
  33520   33580   33600   33640   33700   33720   33800   33810 
      2       1      47       1      15       1      25       1 
  33820   33850   33900   33950   34000   34001   34004   34010 
      1       1      21       2     272       1       1       3 
  34020   34050   34080   34100   34110   34130   34200   34204 
      2       1       1      16       1       1      28       1 
  34290   34300   34301   34310   34330   34340   34350   34400 
      1      30       1       1       1       1       1      19 
  34420   34430   34500   34520   34550   34580   34600   34700 
      1       1      37       1       2       1      22      13 
  34800   34804   34820   34900   34950   35000   35001   35010 
     41       1       1      29       1     953       2       3 
  35020   35030   35050   35060   35100   35104   35110   35120 
      7       2       4       1      24       1       1       1 
  35130   35150   35200   35201   35290   35300   35301   35310 
      1       1      33       1       1      21       1       1 
  35320   35360   35400   35470   35490   35500   35520   35530 
      2       2      29       2       1      31       2       1 
  35550   35570   35600   35670   35700   35740   35760   35780 
      1       1      27       1      15       1       1       1 
  35800   35804   35830   35860   35900   35960   36000   36001 
     24       1       1       1      20       2     493       1 
  36004   36010   36020   36030   36050   36100   36110   36200 
      4       1       2       2       3      19       1      24 
  36260   36300   36320   36350   36400   36401   36430   36440 
      1      20       1       1      38       1       1       1 
  36480   36490   36500   36520   36600   36601   36620   36650 
      1       1      42       1      25       1       1       1 
  36700   36800   36810   36850   36900   37000   37001   37010 
     26      30       1       1      20     237       1       1 
  37030   37100   37110   37120   37140   37150   37200   37260 
      2      20       1       2       1       2      32       1 
  37300   37350   37400   37430   37460   37500   37540   37590 
     19       1      40       1       1      48       1       1 
  37600   37700   37770   37800   37804   37810   37820   37840 
     25      16       1      30       1       1       1       1 
  37850   37900   37910   37920   38000   38010   38020   38030 
      2      14       1       1     459       2       2       1 
  38040   38050   38070   38080   38100   38120   38150   38180 
      1       2       1       1      17       1       4       2 
  38200   38220   38250   38260   38300   38390   38400   38401 
     19       1       2       1      18       1      49       1 
  38410   38450   38500   38600   38601   38620   38690   38700 
      1       1      36      23       1       1       1      13 
  38710   38780   38800   38810   38850   38900   38901   38930 
      1       1      21       1       2      22       1       1 
  39000   39001   39004   39010   39030   39080   39100   39104 
    217       1       2       1       1       1      18       1 
  39150   39200   39250   39270   39280   39300   39400   39450 
      2      30       1       1       1      16      18       1 
  39470   39480   39500   39510   39600   39610   39620   39650 
      1       1      39       1      29       1       2       3 
  39700   39800   39850   39900   39901   39920   39990   40000 
     17      14       3      10       1       1       1    1407 
  40004   40010   40020   40030   40040   40050   40060   40080 
      2       3       7       2       1       3       2       2 
  40090   40100   40120   40130   40150   40180   40200   40240 
      1      27       1       1       1       1      21       1 
  40250   40290   40300   40360   40380   40400   40500   40510 
      1       1      19       1       1      20      23       1 
  40530   40600   40700   40701   40704   40730   40800   40900 
      2      17      17       1       2       1      31      12 
  40904   40910   40960   41000   41020   41030   41100   41110 
      1       1       1     193       1       1      10       1 
  41120   41130   41200   41300   41350   41400   41430   41450 
      1       1      28      12       1      20       1       1 
  41500   41520   41530   41540   41570   41600   41620   41650 
     27       1       1       1       1      47       1       1 
  41700   41800   41810   41820   41900   41920   41950   41960 
     13      18       1       2      19       1       1       1 
  42000   42001   42010   42020   42040   42080   42100   42120 
    472       2       1       2       1       1      18       3 
  42130   42150   42200   42210   42220   42300   42380   42400 
      2       1      19       1       1      28       1      15 
  42450   42460   42500   42504   42510   42550   42600   42700 
      1       1      32       1       1       2      19      11 
  42750   42770   42800   42900   42920   42950   42960   43000 
      1       1      18      17       1       1       1     217 
  43001   43050   43060   43100   43110   43200   43220   43260 
      2       2       2      13       1      20       1       1 
  43300   43360   43400   43430   43480   43500   43560   43580 
     10       1      20       2       1      25       1       1 
  43600   43700   43704   43730   43800   43840   43880   43890 
     21      19       1       1      20       1       2       1 
  43900   44000   44004   44020   44060   44100   44104   44150 
      5     175       1       1       1      13       1       1 
  44180   44200   44270   44300   44320   44350   44400   44410 
      1      16       1      13       1       1      28       1 
  44440   44450   44460   44500   44600   44610   44620   44690 
      1       1       1      17      19       1       1       1 
  44700   44730   44760   44800   44810   44820   44880   44900 
      5       1       1      18       1       1       1      12 
  45000   45001   45004   45010   45020   45030   45040   45080 
    835       1       1       3       4       2       1       1 
  45100   45130   45150   45180   45200   45300   45400   45450 
     17       1       1       1      18      18      15       2 
  45490   45500   45600   45620   45630   45640   45650   45700 
      1      28      27       1       1       1       1      17 
  45790   45800   45860   45900   45960   45980   46000   46020 
      1      17       1      12       1       1     189       1 
  46050   46070   46080   46100   46130   46200   46240   46300 
      3       1       1      12       1      20       1      12 
  46340   46400   46401   46450   46500   46560   46600   46670 
      1      18       1       1      20       1      15       1 
  46700   46720   46760   46800   46804   46850   46860   46870 
     11       1       1      14       1       1       1       1 
  46880   46900   46950   47000   47004   47010   47020   47050 
      1      14       1     189       1       4       1       2 
  47100   47120   47130   47150   47160   47200   47201   47210 
     12       1       1       1       1      19       1       1 
  47250   47300   47390   47400   47500   47580   47600   47620 
      1      16       1      16      29       1      15       1 
  47690   47700   47720   47800   47850   47900   48000   48001 
      1      14       1      11       2      11     378       1 
  48010   48020   48040   48100   48110   48180   48200   48300 
      1       2       1      16       1       1      17       5 
  48320   48400   48440   48450   48500   48550   48600   48700 
      1      18       1       2      23       2      14       8 
  48720   48800   48820   48860   48880   48900   48910   48990 
      1      15       1       1       1       8       1       1 
  49000   49001   49004   49010   49030   49040   49050   49080 
    127       2       1       1       1       1       1       1 
  49100   49150   49200   49210   49300   49320   49400   49500 
     11       1      20       1      14       1      15      27 
  49530   49600   49650   49680   49700   49720   49750   49800 
      1      17       1       1       5       1       1      11 
  49830   49900   49920   49950   50000   50001   50004   50010 
      1      22       1       1    1375       4       3       5 
  50020   50030   50040   50050   50060   50100   50130   50150 
      2       3       1       2       1      15       1       1 
  50170   50180   50190   50200   50210   50300   50330   50340 
      1       1       1      20       2      11       1       1 
  50380   50400   50430   50450   50500   50530   50550   50580 
      1      14       2       1      15       1       1       1 
  50600   50650   50660   50690   50700   50800   50850   50900 
     13       1       1       1       8      10       1      14 
  51000   51020   51030   51060   51100   51120   51150   51200 
    174       1       1       2       8       2       1      12 
  51210   51250   51300   51330   51340   51360   51370   51400 
      1       1      11       1       1       1       1       9 
  51490   51500   51540   51600   51604   51650   51680   51700 
      1      18       1      23       1       1       1       7 
  51750   51780   51800   51850   51890   51900   52000   52010 
      1       2       9       1       1       8     422       2 
  52020   52040   52050   52070   52100   52150   52200   52220 
      2       2       1       2      11       2      16       1 
  52230   52300   52350   52400   52420   52500   52530   52550 
      1       5       1      10       1      13       1       1 
  52600   52650   52700   52710   52740   52750   52800   52850 
     13       2       7       1       1       1      25       2 
  52900   52930   53000   53001   53010   53040   53050   53100 
      8       1     187       3       3       1       2       8 
  53200   53250   53300   53340   53400   53500   53600   53640 
     10       1       4       1      12       9       4       1 
  53700   53760   53800   53880   53900   53904   54000   54001 
      5       1       8       1       5       1     253       1 
  54004   54010   54020   54030   54040   54050   54060   54100 
      2       1       1       1       2       2       1       7 
  54150   54200   54300   54390   54400   54500   54590   54600 
      2       6       8       1       8       7       1       2 
  54650   54680   54700   54790   54800   54830   54880   54900 
      1       1       9       1      10       1       1      11 
  55000   55004   55010   55020   55030   55050   55060   55080 
    565       1       4       1       3       6       1       1 
  55090   55100   55120   55150   55200   55250   55300   55400 
      1      11       1       1      19       1       5       9 
  55500   55600   55700   55750   55800   55850   55900   56000 
      7      11      11       1       9       1       7     219 
  56020   56030   56060   56070   56100   56130   56140   56150 
      1       2       1       1       4       1       1       1 
  56200   56210   56300   56330   56400   56420   56500   56600 
     10       1       9       1       8       1      10       9 
  56601   56604   56700   56800   56900   56940   57000   57004 
      1       1       5       9       5       1     176       1 
  57010   57020   57040   57100   57200   57300   57350   57360 
      1       2       1       5       8       5       1       1 
  57400   57450   57500   57510   57600   57700   57800   57900 
      9       1      14       1      18      11       7       7 
  58000   58001   58004   58010   58020   58030   58040   58050 
    201       1       3       1       1       1       1       2 
  58100   58110   58130   58170   58200   58300   58310   58400 
      7       1       1       1      13       4       1       6 
  58500   58570   58600   58680   58700   58800   58900   59000 
     13       1       5       1       5       6       3     115 
  59030   59100   59200   59250   59260   59280   59300   59340 
      1       6       2       1       1       1       6       1 
  59400   59500   59550   59600   59640   59700   59800   59810 
      3      11       1       9       1       5       5       1 
  59840   59900   60000   60001   60004   60020   60040   60050 
      1       4    1060       3       1       5       2       6 
  60070   60080   60100   60110   60120   60200   60210   60220 
      1       1      11       1       1      13       1       1 
  60250   60300   60350   60380   60400   60460   60500   60600 
      1       7       1       2       3       1      15       9 
  60700   60800   60820   60850   60900   60950   60980   61000 
      4       7       1       1       6       1       1     101 
  61010   61030   61050   61100   61160   61200   61300   61330 
      1       1       1       9       1      15       4       1 
  61350   61400   61500   61600   61650   61700   61750   61800 
      1       6       9       4       1       5       1       7 
  61830   61900   61940   62000   62001   62004   62010   62040 
      1       2       1     197       1       2       3       2 
  62050   62070   62100   62200   62210   62250   62300   62400 
      3       1       5      10       1       1       7      16 
  62430   62500   62510   62600   62700   62800   62900   63000 
      1       7       1       7       7       5       3     154 
  63020   63030   63050   63060   63100   63120   63200   63250 
      1       1       1       1       7       1      10       1 
  63300   63400   63420   63480   63500   63520   63530   63600 
      7       5       1       1      11       1       1       9 
  63601   63650   63700   63800   63850   63900   64000   64001 
      1       1       4       4       1       3     123       2 
  64010   64020   64040   64060   64100   64200   64300   64400 
      1       1       1       1       3       6       5       3 
  64440   64500   64600   64700   64710   64800   64900   65000 
      1       4       8       4       1       5       4     590 
  65001   65004   65010   65020   65030   65050   65080   65090 
      1       3       4       5       1       6       2       1 
  65100   65120   65140   65150   65200   65250   65280   65290 
      8       1       1       1       9       3       1       1 
  65300   65320   65350   65380   65400   65450   65500   65590 
      7       1       1       1       5       1      10       1 
  65600   65700   65800   65850   65860   65900   66000   66004 
      5       3       9       1       1       8      97       2 
  66010   66030   66050   66080   66100   66200   66280   66300 
      1       1       2       1       6       6       1      10 
  66400   66500   66600   66660   66700   66800   66900   66970 
      4      14      11       1       7      10       1       1 
  67000   67001   67010   67060   67100   67140   67150   67170 
    123       1       3       1       4       1       2       1 
  67200   67280   67300   67400   67500   67600   67700   67800 
     13       1      11       6       7       5       5       6 
  67870   67900   68000   68001   68030   68060   68100   68140 
      1       3     187       1       1       1       6       1 
  68200   68300   68400   68500   68600   68700   68800   68900 
      5       2       6       4      10       4      10       3 
  68950   69000   69010   69030   69100   69200   69300   69400 
      1     102       1       1       2       7       6       5 
  69500   69600   69700   69800   69900   70000   70001   70004 
      4       7       4       9       7     630       3       2 
  70010   70020   70030   70040   70050   70060   70090   70100 
      5       3       2       2       3       3       1      11 
  70110   70130   70150   70180   70200   70300   70310   70350 
      1       1       1       1       7       3       1       1 
  70400   70500   70520   70600   70660   70700   70800   70900 
      6       8       1       4       2       1       7       4 
  71000   71004   71020   71050   71100   71110   71150   71200 
     79       3       1       2       6       1       2       9 
  71300   71400   71460   71500   71520   71530   71560   71600 
      7       6       1       7       1       1       1       9 
  71700   71750   71800   71850   71900   72000   72004   72030 
      1       2       5       1       2     194       3       1 
  72050   72100   72180   72200   72240   72300   72320   72350 
      1       1       1       7       1       3       1       1 
  72400   72410   72500   72550   72600   72700   72800   72840 
     11       1       5       1       9      10       7       1 
  72900   73000   73001   73004   73010   73020   73030   73050 
      1      96       1       1       1       1       1       1 
  73100   73200   73220   73270   73300   73400   73440   73500 
      8       2       1       1       5       1       1       5 
  73600   73700   73750   73800   73900   74000   74030   74100 
      6       5       1       9       2      94       1       6 
  74140   74200   74250   74260   74300   74400   74500   74510 
      1      10       1       1       3       8       2       1 
  74550   74600   74660   74700   74704   74740   74800   74900 
      1       8       1       4       1       1       7       3 
  74940   75000   75001   75004   75010   75020   75030   75040 
      1     465       1       1       5       1       3       1 
  75050   75080   75100   75150   75180   75200   75204   75220 
      1       1       5       3       1       3       1       1 
  75250   75280   75300   75400   75500   75530   75600   75700 
      1       1       8       5       9       1       3       6 
  75710   75800   75900   76000   76004   76020   76040   76200 
      1       5       3      99       1       1       1       9 
  76300   76400   76500   76540   76600   76700   76800   76850 
      8       2       9       1       5       4       3       1 
  76900   77000   77100   77200   77300   77400   77500   77520 
      2      88       2       3       6       3       3       1 
  77600   77620   77650   77690   77700   77800   77840   77900 
      5       1       1       1       3       1       1       3 
  78000   78010   78020   78050   78100   78200   78300   78400 
    123       1       2       3       8       8       6       2 
  78500   78600   78650   78700   78800   78810   79000   79010 
      2       7       1       5       3       2      43       1 
  79030   79080   79100   79200   79250   79300   79304   79340 
      2       1       2       2       1       2       1       1 
  79400   79430   79500   79520   79600   79630   79700   79800 
      6       1       6       1       4       1       3       8 
  79850   79900   79920   79940   80000   80001   80010   80020 
      1       3       1       1     629       4       3       2 
  80050   80080   80100   80110   80120   80150   80170   80200 
      3       1       6       2       2       1       1       6 
  80230   80250   80300   80350   80400   80500   80510   80600 
      2       1       2       1       2       5       1       3 
  80700   80800   80900   81000   81100   81120   81200   81300 
      4       4       2      61       1       1       6       3 
  81350   81400   81450   81500   81600   81660   81700   81800 
      1       3       1       5       3       1       2       4 
  81900   82000   82004   82040   82100   82130   82200   82300 
      4     106       1       1       3       1       4       3 
  82400   82420   82500   82600   82800   82900   82970   82990 
      2       1       1       4      10       6       1       1 
  83000   83001   83004   83020   83030   83040   83060   83070 
     69       1       2       3       1       1       1       1 
  83080   83100   83200   83220   83300   83400   83500   83600 
      1       2       8       1       1       3       3       3 
  83700   83800   83900   84000   84001   84020   84100   84110 
      3       4       1      80       1       2       3       1 
  84200   84220   84300   84400   84404   84430   84440   84500 
      5       1       6       3       1       1       1       5 
  84600   84670   84700   84800   84850   84900   85000   85010 
      4       1       3       7       1       2     273       4 
  85020   85030   85050   85060   85090   85100   85200   85250 
      3       3       1       1       1       4      10       1 
  85280   85300   85400   85500   85600   85800   85810   85830 
      1       3       4      10       3       5       1       1 
  85840   85900   86000   86004   86010   86100   86150   86200 
      1       4      73       1       1       2       1       3 
  86300   86400   86470   86500   86504   86510   86600   86650 
      5       5       1       5       1       1       3       1 
  86800   86900   87000   87030   87040   87100   87150   87180 
      4       5      69       2       1       5       1       1 
  87200   87300   87470   87500   87600   87700   87800   87820 
      6       1       1       9       1       1       3       1 
  88000   88001   88020   88050   88070   88100   88200   88260 
     77       1       1       2       2       2       4       1 
  88300   88400   88420   88450   88500   88600   88800   88810 
      2       3       1       1       3       4       2       1 
  88900   89000   89020   89030   89040   89100   89190   89200 
      2      77       1       2       1       1       1       2 
  89300   89400   89480   89500   89600   89700   89800   89900 
      1       3       2       2       4       2       3       2 
  89930   90000   90001   90004   90010   90020   90030   90050 
      1     373       1       1       1       1       1       1 
  90060   90090   90100   90150   90200   90300   90350   90400 
      2       1       6       2       7       5       1       4 
  90450   90500   90600   90700   90800   90900   90920   91000 
      1       5       4       2       4       1       1      59 
  91050   91100   91120   91200   91250   91300   91400   91450 
      1       2       1       7       1       3       2       1 
  91500   91520   91600   91650   91700   91800   91900   92000 
      5       1       5       1       1       2       1      91 
  92004   92020   92040   92050   92100   92200   92220   92240 
      1       1       1       1       6       4       1       1 
  92300   92400   92440   92500   92800   93000   93020   93050 
      1       2       1       7       4      47       1       2 
  93100   93200   93300   93400   93430   93500   93550   93600 
      5       4       1       1       1       3       1       1 
  93700   93850   93900   94000   94001   94090   94100   94200 
      3       1       1      59       2       1       3       1 
  94300   94400   94500   94600   94700   94800   95000   95020 
      1       2       1       1       3       1     156       3 
  95050   95100   95150   95200   95240   95250   95300   95400 
      1       4       1       3       1       1       3       1 
  95500   95600   95650   95700   95721   95730   95800   95900 
      3       1       1       1       1       1       1       1 
  96000   96001   96010   96120   96150   96200   96250   96390 
     65       1       1       1       1       4       2       1 
  96400   96440   96500   96600   96650   96700   96740   96750 
      1       1       4       2       1       4       1       1 
  96800   96900   97000   97050   97090   97100   97150   97200 
      2       3      56       1       1       2       1       2 
  97300   97400   97500   97700   97900   98000   98001   98010 
      1       4       6       2       2      87       1       2 
  98020   98030   98100   98150   98200   98400   98500   98600 
      3       1       2       1       2       4       9       4 
  98700   98800   98900   98950   99000   99030   99200   99300 
      6       2       1       1      36       1       2       3 
  99400   99420   99500   99520   99700   99710   99800   99900 
      1       1       4       1       1       1       3       2 
 100000  100001  100004  100010  100020  100030  100080  100100 
    563       3       4       4       5       8       1      11 
 100110  100120  100180  100200  100250  100300  100330  100380 
      1       1       1       5       1       5       1       1 
 100400  100470  100500  100600  100700  100750  100800  100900 
      4       1       9       1       4       1       3       4 
 101000  101004  101050  101060  101100  101120  101200  101300 
     40       1       1       1       2       1       3       1 
 101350  101480  101500  101600  101700  101800  102000  102030 
      1       1       6       6       2       2      55       1 
 102080  102200  102300  102310  102320  102400  102500  102600 
      1       5       1       1       1       1       1       3 
 102630  102650  102800  102900  102950  102980  103000  103010 
      1       1       4       1       1       1      53       1 
 103020  103050  103100  103150  103300  103400  103600  103610 
      1       1       6       1       1       2       4       1 
 103640  103700  103800  103900  104000  104004  104040  104100 
      1       1       3       1      40       1       1       1 
 104180  104200  104220  104300  104500  104600  104770  104800 
      1       3       1       2       1       1       1       2 
 105000  105001  105020  105030  105060  105100  105200  105350 
    127       2       1       1       1       4       6       1 
 105400  105500  105600  105800  105810  105900  105920  106000 
      2       1       3       1       1       1       1      39 
 106004  106010  106020  106040  106060  106100  106200  106280 
      1       1       1       1       1       2       2       1 
 106400  106500  106600  106700  107000  107004  107030  107100 
      1       4       3       2      38       1       1       2 
 107200  107330  107400  107500  107600  107700  107800  107950 
      1       1       1       1       2       5       1       1 
 108000  108010  108100  108200  108220  108400  108500  108600 
     46       1       2       2       1       3       1       2 
 108700  108800  108900  109000  109140  109160  109200  109210 
      2       1       1      31       1       1       2       1 
 109300  109400  109500  109600  109610  109700  109800  110000 
      1       3       2       1       1       1       3     188 
 110004  110010  110030  110040  110100  110200  110500  110520 
      1       2       1       1       5       1       6       1 
 110600  110670  110700  110800  110900  111000  111001  111100 
      1       1       1       4       1      22       1       1 
 111200  111260  111300  111360  111400  111600  111700  111800 
      2       1       1       1       2       2       1       2 
 111890  111900  112000  112020  112060  112100  112200  112280 
      1       1      33       1       1       3       1       1 
 112300  112400  112440  112500  112600  112700  112800  112830 
      3       1       1       3       1       3       2       1 
 112850  113000  113080  113100  113400  113500  113600  113700 
      1      33       1       1       2       4       1       2 
 113800  113900  113940  114000  114020  114060  114100  114200 
      4       3       1      28       1       1       2       2 
 114400  114500  114600  114800  114900  114920  115000  115010 
      4       2       3       3       1       1     116       1 
 115020  115070  115100  115180  115200  115300  115320  115400 
      1       1       6       1       4       2       1       1 
 115450  115500  115600  115700  115790  115820  115900  116000 
      1       2       2       1       1       1       1      25 
 116010  116030  116100  116140  116200  116300  116400  116700 
      1       1       1       1       2       2       3       2 
 116800  116900  116930  117000  117030  117170  117200  117300 
      1       1       1      27       1       1       2       1 
 117400  117500  117700  118000  118100  118200  118420  118500 
      3       2       1      23       1       2       1       2 
 118600  118700  118760  118800  119000  119200  119300  119500 
      1       3       1       1      19       1       1       1 
 119530  119600  119700  119800  119900  120000  120004  120010 
      1       5       1       1       1     290       1       1 
 120020  120070  120100  120200  120240  120250  120300  120400 
      2       2       5       5       2       2       4       1 
 120500  120600  120700  120800  120901  121000  121050  121100 
      1       1       1       2       1      27       1       1 
 121200  121400  121500  121600  121900  122000  122030  122070 
      1       2       3       5       1      25       1       1 
 122100  122200  122300  122400  122500  122600  123000  123060 
      1       3       1       4       2       1      14       1 
 123100  123200  123300  123500  123600  123800  124000  124060 
      1       2       1       1       1       2      22       1 
 124100  124200  124250  124300  124320  124500  124800  124900 
      2       1       1       1       1       1       4       1 
 125000  125030  125050  125090  125100  125200  125300  125400 
    122       1       1       1       2       2       2       1 
 125500  125600  125900  126000  126030  126110  126130  126200 
      2       2       2      25       1       1       1       2 
 126300  126350  126400  126550  126800  127000  127050  127100 
      2       1       2       1       2      18       1       1 
 127400  127500  127700  127800  127840  128000  128200  128300 
      2       1       2       4       1      19       1       1 
 128500  128600  128900  129000  129030  129100  129200  129240 
      3       1       1      16       1       1       3       1 
 129410  129600  129800  130000  130001  130010  130020  130030 
      1       3       2     153       1       1       2       3 
 130040  130120  130200  130300  130400  130500  130570  130600 
      1       1       1       2       1       3       1       1 
 131000  131200  131400  131600  131800  131900  132000  132040 
     12       3       1       2       1       1      21       1 
 132100  132200  132400  132600  132700  133000  133010  133100 
      3       1       2       1       1      15       1       1 
 133200  133300  133500  133600  133700  133800  133950  134000 
      4       1       1       1       1       1       1      15 
 134010  134050  134100  134300  134400  134500  134600  134700 
      1       1       1       2       1       3       1       1 
 134800  134900  135000  135001  135010  135030  135200  135300 
      3       1      65       2       1       2       1       2 
 135400  135500  135600  135800  136000  136010  136060  136200 
      3       3       2       2      21       1       1       1 
 136300  136400  136500  136900  137000  137100  137300  137400 
      2       1       1       1       8       1       2       1 
 137600  137800  138000  138100  138200  138250  138300  138400 
      1       1      14       2       1       1       1       2 
 138500  139000  139030  139500  139600  139700  139800  140000 
      2      10       1       1       1       1       1     131 
 140001  140010  140030  140050  140100  140120  140190  140500 
      2       1       2       2       2       1       1       4 
 140700  140800  140900  140940  141000  141200  141400  141500 
      1       1       2       1      10       3       1       4 
 141600  141700  141800  142000  142100  142400  142500  143000 
      3       1       1      15       1       2       1      14 
 143100  143400  143800  144000  144040  144100  144200  144400 
      2       1       1      16       1       2       1       2 
 144600  144700  144800  145000  145030  145100  145150  145200 
      1       1       1      44       1       3       1       2 
 145250  145400  145450  145500  145600  145660  145700  146000 
      1       2       1       1       2       1       1      13 
 146004  146120  146200  146240  146600  146800  147000  147200 
      1       1       2       1       1       1      11       1 
 147210  147300  147400  147500  147600  147900  148000  148100 
      1       2       1       1       1       1      11       1 
 148200  148250  148400  148500  148600  148800  148900  149000 
      1       1       1       1       3       1       1      10 
 149020  149100  149200  149400  149600  149780  150000  150001 
      1       1       1       1       1       1     220       1 
 150004  150010  150020  150030  150040  150100  150150  150160 
      1       1       1       1       1       5       1       1 
 150200  150250  150300  150500  150690  150800  150900  151000 
      2       2       1       3       1       1       1       9 
 151100  151400  151600  151900  152000  152020  152100  152120 
      1       2       1       1       9       1       1       1 
 152300  152320  152600  152900  153000  153200  153500  153900 
      1       1       3       1       7       1       2       1 
 154000  154240  154300  154500  154600  154800  155000  155001 
      9       1       1       2       1       1      34       1 
 155020  155030  155140  155200  155250  155500  155600  155820 
      1       1       1       2       1       2       1       1 
 156000  156200  156500  157000  157200  157400  157500  157600 
      8       1       1       9       2       1       2       1 
 158000  158004  158100  158500  158600  158900  159000  160000 
     12       1       1       2       2       1       5      84 
 160001  160050  160100  160160  160200  160400  160500  160600 
      1       1       2       1       2       1       1       2 
 160800  161000  161200  161300  161400  161600  161700  161900 
      1       8       1       1       1       2       2       1 
 162000  162080  162100  162400  162500  162650  163000  163100 
     15       1       1       1       1       1       6       1 
 163200  163400  163550  163650  163700  163900  164000  164400 
      3       1       1       1       3       1      12       3 
 164500  164600  165000  165060  165100  165150  165300  165400 
      2       1      28       1       1       1       1       1 
 165500  165600  166000  166400  166630  167000  167100  167500 
      1       1       6       1       1      10       1       1 
 167800  168000  168700  168780  169000  169500  169700  170000 
      1       7       1       1      10       2       3      48 
 170001  170050  170100  170260  170300  170350  170400  170500 
      1       1       1       1       1       1       1       1 
 171000  171200  171300  171800  172000  172300  173000  173100 
      6       1       1       1       7       1       5       1 
 173200  173300  173400  173500  173600  174000  174300  174400 
      1       1       1       1       1       4       1       1 
 174560  174600  175000  175100  175200  175300  175500  175600 
      1       1      49       2       1       1       1       1 
 176000  176050  176200  176400  176500  177000  177300  177400 
      5       1       1       1       3       3       1       1 
 177500  177600  177700  177800  178000  178500  178800  178900 
      2       1       1       1       5       1       2       1 
 179000  179100  180000  180001  180100  180200  180250  180300 
      7       1      72       1       1       3       1       2 
 180500  180600  180700  181000  181100  181200  181400  181500 
      4       1       1       9       2       2       1       1 
 181600  181700  181900  182000  182160  182200  182300  182800 
      1       1       1       4       1       1       1       1 
 183000  183150  183500  184000  184600  184990  185000  185020 
      5       1       1       2       1       1      27       1 
 185100  185200  185300  185710  185800  186000  186200  186500 
      1       1       1       1       1       6       2       2 
 186600  186700  186800  187000  187200  187700  187800  187900 
      1       1       1       8       1       1       2       1 
 188000  188500  188900  189000  189200  189450  189500  189600 
      4       1       1       6       1       1       1       1 
 189700  190000  190100  190120  190150  190200  190300  190500 
      1      26       2       2       1       1       1       1 
 190970  191000  192000  192250  192500  192600  192800  193000 
      1       5       4       1       1       1       1       3 
 194000  194100  194400  194500  195000  195100  195200  195300 
      9       1       1       1      18       1       1       1 
 195600  195800  196000  196400  197000  197080  197400  197500 
      1       1       2       1       6       1       1       1 
 197800  198000  198700  199000  199050  199500  199600  200000 
      1       5       1       1       1       1       1     111 
 200100  200200  200250  200300  200500  200750  200800  201000 
      1       1       1       1       4       1       1      10 
 201100  201290  201400  201500  201600  202000  202500  203000 
      1       1       1       2       1       6       3       9 
 203500  203600  203900  204000  204001  204400  204500  205000 
      3       1       1       5       1       1       1      11 
 205100  205400  205700  206000  206900  207000  207200  208000 
      2       1       1       1       1       6       1       5 
 208600  209000  210000  210070  210200  210500  211000  211100 
      1       5      31       1       1       1       4       1 
 211200  211700  211900  212000  212050  212800  213000  213100 
      1       1       1       7       1       1       4       2 
 213400  214000  214400  215000  215500  215600  216000  216500 
      1       4       1       6       1       1       5       1 
 216700  217000  217400  217500  218000  218200  219000  219400 
      1       4       1       2       3       2       2       1 
 219700  220000  220100  220130  221300  221600  221700  222000 
      1      31       2       1       1       1       1       2 
 222300  222400  222700  223000  223400  223800  223900  224000 
      1       1       1       1       1       1       1       1 
 225000  225200  225300  225400  225500  226000  227000  227200 
     23       1       1       1       2       1       6       1 
 227400  227600  228000  228200  228300  228370  229000  229100 
      1       1       5       1       1       1       1       1 
 229600  230000  230120  230400  231000  232000  232050  232300 
      1       8       1       1       4       3       1       1 
 232600  233000  233400  233500  234000  234200  234500  235000 
      1       2       1       1       1       2       1       3 
 235100  235200  235500  235900  236000  236400  236600  237000 
      2       1       1       1       3       1       1       6 
 237100  237800  238000  238200  238300  239000  239700  239800 
      1       2       2       1       1       2       1       1 
 240000  240001  240200  240500  241000  242000  242100  243000 
     15       1       1       1       3       1       1       5 
 243100  243800  243900  244000  244200  244500  245000  245140 
      1       2       1       5       1       1      10       1 
 245500  246000  246400  246800  247000  248000  249000  249700 
      1       2       1       1       1       7       1       1 
 249800  250000  250100  250300  250800  251000  251200  251400 
      1      54       2       1       2       2       2       1 
 251500  251600  252000  253000  253410  253800  254000  255000 
      1       1       3       2       1       5       1       5 
 255460  256000  256800  257000  257700  258000  258400  258600 
      1       2       1       3       1       7       1       1 
 259600  259900  260000  260500  261000  261600  262970  263000 
      1       2       8       1       2       2       1       3 
 263400  263700  263800  264000  265000  265400  265800  266000 
      1       1       1       1       2       2       1       3 
 266500  267000  267100  268000  268300  269000  269500  269600 
      2       1       1       3       1       1       1       1 
 270000  270100  270700  270900  271000  271700  272000  272200 
      8       2       1       1       1       1       2       1 
 272600  273000  273550  273600  274000  274900  275000  275100 
      1       1       1       1       3       1       6       1 
 275300  275400  276000  276400  277000  277700  278000  278400 
      1       1       4       1       1       1       3       1 
 278500  279000  279900  280000  280800  281800  282000  283000 
      1       4       1       5       1       1       1       1 
 283200  283300  283500  284800  285000  285500  286000  286500 
      1       1       1       1       3       1       2       1 
 287000  287500  288000  289000  289500  289600  289800  290000 
      1       1       7       4       1       1       1       3 
 290400  291000  291500  293000  293400  294000  294400  295000 
      1       3       1       1       1       2       1       3 
 297000  297500  298000  298500  299000  299100  299600  300000 
      2       1       1       1       1       1       1      14 
 300050  300300  300400  300900  301000  301100  301500  302000 
      1       1       1       1       1       1       1       2 
 303000  303100  303400  304200  305000  306000  307000  307400 
      1       1       1       1       3       3       3       1 
 308000  308500  308950  309000  309700  309800  310000  311000 
      9       1       1       3       1       1       2       4 
 312000  313000  313400  314000  314400  315000  315200  315800 
      3       2       1       3       1       5       1       1 
 316000  316600  317000  317300  318000  320000  320500  321000 
      1       3       1       1       1       2       1       1 
 322000  322100  322800  323000  324000  324200  325000  325200 
      3       1       1       1       3       1       3       1 
 325900  326000  326900  327000  328000  329000  329100  329600 
      2       1       1       2       3       2       1       1 
 330000  331000  331100  331200  332000  333000  335000  335100 
      3       5       1       1       4       1       1       1 
 335800  336600  338000  339000  339730  340000  340900  341000 
      1       1       2       5       1       4       1       9 
 341060  342000  343000  343500  343800  344000  344500  345000 
      1       1       1       1       1       3       1       1 
 345100  345300  346000  347000  347050  348000  349000  349500 
      1       1       2       3       1       1      15       1 
 350000  350200  351000  351400  352000  352100  353000  353200 
      6       1       2       1       2       1       2       1 
 355000  356000  357000  357300  358000  358500  360000  360300 
      2       2       1       1       1       1       1       1 
 360600  362000  362700  363000  364000  365000  366000  368000 
      1       1       1       4       1       1       1       1 
 369000  369500  370000  371000  371050  372700  373000  374000 
      1       1       1       1       1       1       1      11 
 374100  376000  377000  378000  379000  380000  381000  383000 
      1       1       1       3       1       3       2       6 
 385000  385001  385070  386000  386900  387000  387001  389000 
      2       1       1       1       1       1       1       1 
 389300  389400  391000  393000  395300  396000  396001  396100 
      1       1       1       1       1       8       1       1 
 398000  399000  399200  400000  401000  402500  402800  403000 
      6       1       1       1       1       1       1       1 
 403400  403600  406000  406330  407600  407700  408000  408500 
      1       1       9       1       1       1       2       1 
 410000  412000  412900  414000  414500  415000  416000  418000 
      2       5       1       2       1       3       1      43 
 418110  418300  418400  418430  418500  419000  420000  420500 
      1       1       1       1       1       9       4       1 
 422000  422100  423000  424000  425000  426000  426100  426500 
     12       1       2       2       2      19       1       1 
 427000  427800  428000  428200  428500  429000  430500  430700 
      4       1       4       1       2       9       1       1 
 431000  432000  432010  433000  433300  433800  434000  434890 
      3       1       1      15       1       1       2       1 
 435000  437000  437200  438000  439000  441000  441700  442000 
      3       1       1       5       1       2       1       1 
 443150  444500  445000  446000  447000  447500  448000  448800 
      1       1       1       1       1       1       1       1 
 449000  450000  451000  454000  454600  456000  457000  458000 
      1       1       1       7       1       1       1       7 
 458400  458500  459000  462000  464000  466000  466100  467000 
      1       1       1       1       1       3       1       4 
 467600  468000  469000  470700  472000  474000  479000  483000 
      1       2       1       1       1       1       2       1 
 488000  488200  490000  491000  492000  494000  498600  499000 
      1       1       1       2       3       1       1       1 
 502000  502030  502050  502500  502900  504000  504400  505200 
     12       1       1       1       1      36       2       1 
 505220  506000  506100  506300  506500  507000  507500  508000 
      1      10       1       1       1       2       1       5 
 508200  509000  511000  511500  512000  514000  515000  519000 
      1       2       3       1       1       3       1       1 
 520000  521000  523000  526000  526450  529000  531000  532000 
      1       1       1       2       1       1       2       2 
 535500  537000  539400  543000  545000  546000  546800  547000 
      1       1       1       7       1       1       1       2 
 554000  557000  558000  559000  562000  568000  570000  575000 
      1       1       1       2       1       1       1       1 
 580000  582000  583000  584000  584700  585000  586000  588800 
      1       1       3       2       1       1       1       1 
 593000  597000  599000  600000  601000  601160  601300  602000 
      1       1       1       1      18       1       1       1 
 602500  603000  604410  609000  611000  615100  626400  627000 
      1       3       1       1       1       1       1       1 
 636000  657000  661000  665000  666000  690000  694000  704000 
      1       1       1       4       2       1       1       2 
 709600  719000  724000  728000  729000  739000  740000  747000 
      1       1       1       1       1       1       2       1 
 761600  766000  787000  812000  859000  861000  868200  897100 
      1       1       1       3       1       1       1       1 
 997000 1051000 1257000    <NA> 
      1       2       1       0 
```

]

- age取值等于0，则转换为缺失值`NA`
- income取值小于0，则转换为缺失值`NA`

<div id="htmlwidget-9a6d99474a86cc410e7b" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-9a6d99474a86cc410e7b">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10"],[1274,9494,9533,11423,26439,30358,47862,52606,58924,69972],[0,0,0,0,0,0,0,0,0,0],[null,null,null,null,null,null,null,null,null,null],[0,0,0,0,0,0,0,0,0,0],["NA","NA","NA","NA","NA","NA","NA","NA","NA","NA"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>id<\/th>\n      <th>age<\/th>\n      <th>age_new<\/th>\n      <th>income<\/th>\n      <th>income_new<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":5,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

]

---

### （税收案例）数据清洗问题——存在缺失值

处理缺失值最简单粗暴的办法就是直接删除行或列，但是这样也会直接去掉很多样本信息：

- 行删除(row delete)
- 列删除(column delete)

]

对于**分类变量**的缺失值，可以直接加一个特定标签（level）。
]

]

对于**数值型变量**的缺失值，可以给缺失值进行**补值**：

- 用均值代替

- 使用各种插值办法

补值后，一定要记得新增加1个变量，指明哪些样本进行了补值操作！

]

]

---

### （税收案例）数据清洗问题——R补值工具

处理前数据集`customer_data`的变量：

```
 [1] "id"                   "custid"              
 [3] "sex"                  "is_employed"         
 [5] "income"               "marital_status"      
 [7] "health_ins"           "housing_type"        
 [9] "recent_move"          "num_vehicles"        
[11] "age"                  "state_of_res"        
[13] "gas_usage"            "gas_with_rent"       
[15] "gas_with_electricity" "no_gas_bill"         
[17] "gas_usage_new"        "age_new"             
[19] "income_new"          
```

]

采用`R`包`vtreat`进行自动补值后新数据集`training_prepared`的变量：

```
 [1] "custid"                     "health_ins"                
 [3] "id"                         "sex"                       
 [5] "is_employed"                "is_employed_isBAD"         
 [7] "income"                     "marital_status"            
 [9] "housing_type"               "recent_move"               
[11] "recent_move_isBAD"          "num_vehicles"              
[13] "num_vehicles_isBAD"         "age"                       
[15] "state_of_res"               "gas_usage"                 
[17] "gas_usage_isBAD"            "gas_with_rent"             
[19] "gas_with_rent_isBAD"        "gas_with_electricity"      
[21] "gas_with_electricity_isBAD" "no_gas_bill"               
[23] "no_gas_bill_isBAD"          "gas_usage_new"             
[25] "gas_usage_new_isBAD"        "age_new"                   
[27] "age_new_isBAD"              "income_new"                
```

]

]

**处理前**的数据缺失情况（4个变量，前6行）：

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<script type="application/json" data-for="htmlwidget-fdac9ff66b145616ad7e">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],[55,65,162,207,219,294],[true,true,null,null,null,null],[null,null,null,null,null,null],[null,null,null,null,null,null],[false,true,false,false,true,true]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>id<\/th>\n      <th>is_employed<\/th>\n      <th>num_vehicles<\/th>\n      <th>housing_type<\/th>\n      <th>health_ins<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

补值工具**处理后**的数据补齐情况（前6行）：

<div id="htmlwidget-f1d17dc5295c58c8e6ed" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-f1d17dc5295c58c8e6ed">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],[55,65,162,207,219,294],[1,1,0.95049275606469,0.95049275606469,0.95049275606469,0.95049275606469],[0,0,1,1,1,1],[2.0654999860222,2.0654999860222,2.0654999860222,2.0654999860222,2.0654999860222,2.0654999860222],[1,1,1,1,1,1],["_invalid_","_invalid_","_invalid_","_invalid_","_invalid_","_invalid_"],[false,true,false,false,true,true]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>id<\/th>\n      <th>is_employed<\/th>\n      <th>is_employed_isBAD<\/th>\n      <th>num_vehicles<\/th>\n      <th>num_vehicles_isBAD<\/th>\n      <th>housing_type<\/th>\n      <th>health_ins<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"targets":2,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n  }"},{"targets":4,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n  }"},{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":["options.columnDefs.0.render","options.columnDefs.1.render"],"jsHooks":[]}</script>

]

---

### （税收案例）数据变换

数据变换主要目的是为让数据能更适合于建模分析（modeling）。

主要变换操作包括：

- 中位数（median）变换

- 均值（mean）变换

- 对数化（log）变换
`$ln(X_i)$`：

- 标准化（sd）变换
`$\frac{(X_i -\bar{X})}{S_{X}}$`

- 把**连续变量**转换为**离散变量**

---

### （税收案例）数据变换：原始收入变量

假设我们还有51个州的**收入的中位数**数据集（`median_income_table`）：

<div id="htmlwidget-a712564d515747a3f3d8" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-a712564d515747a3f3d8">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40","41","42","43","44","45","46","47","48","49","50","51"],["Alabama","Alaska","Arizona","Arkansas","California","Colorado","Connecticut","Delaware","District of Columbia","Florida","Georgia","Hawaii","Idaho","Illinois","Indiana","Iowa","Kansas","Kentucky","Louisiana","Maine","Maryland","Massachusetts","Michigan","Minnesota","Mississippi","Missouri","Montana","Nebraska","Nevada","New Hampshire","New Jersey","New Mexico","New York","North Carolina","North Dakota","Ohio","Oklahoma","Oregon","Pennsylvania","Rhode Island","South Carolina","South Dakota","Tennessee","Texas","Utah","Vermont","Virginia","Washington","West Virginia","Wisconsin","Wyoming"],[21100,32050,26000,22900,25000,32000,36000,29400,40000,24000,24700,30050,22800,27675,25000,27500,30000,22250,20600,28000,36400,35350,25000,32000,20000,25000,30000,30000,25000,33000,32700,20000,27000,24700,29250,26000,23500,25000,28000,30250,25000,28050,25000,25000,29000,33040,30000,30100,21000,30910,34300]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>state_of_res<\/th>\n      <th>median_income<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":8,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[8,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

---

### （税收案例）数据变换：收入变量的中位数变换

现在我们可以，通过如下步骤进行收入的**中位数**变换：

- 把收入的州数据集（`median_income_table`）与前面的案例数据集（`training_prepared`）匹配起来

- 对收入进行中位数变换
`$income\_normalized  =\frac{income_i}{median\_income}$`。

]

下面展示的是用`R`软件进行前述的匹配和计算过程：

```r
mean_income <- round(mean(training_prepared$income, na.rm = T),2)
sd_income <- round(sd(training_prepared$income, na.rm = T),2)

training_prepared <-  training_prepared %>%
* left_join(., median_income_table, by="state_of_res") %>%
* mutate(income_byMedian = income/median_income,
         income_byMean = income/mean_income,
         income_bySd = (income- mean_income)/sd_income,
         income_byLog10 =log10(income))
```

]

最终得到收入的**中位数**变换结果：

<div id="htmlwidget-b1d68c6b0d14057ecaca" style="width:100%;height:auto;" class="datatables html-widget"></div>
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class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>id<\/th>\n      <th>income<\/th>\n      <th>median_income<\/th>\n      <th>income_byMedian<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"targets":4,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatRound(data, 4, 3, \",\", \".\");\n  }"},{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":5,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":["options.columnDefs.0.render"],"jsHooks":[]}</script>

]

---

### （税收案例）数据变换：收入变量的均值变换

现在我们可以，通过如下步骤进行收入的均值变换：

- 对收入进行中位数变换
`$income\_byMean  =\frac{income_i}{\overline{income}}$`。

]

下面展示的是用`R`计算过程：

```r
mean_income <- round(mean(training_prepared$income, na.rm = T),2)
sd_income <- round(sd(training_prepared$income, na.rm = T),2)

training_prepared <-  training_prepared %>%
  left_join(., median_income_table, by="state_of_res") %>% 
  mutate(income_byMedian = income/median_income, 
*        income_byMean = income/mean_income,
         income_bySd = (income- mean_income)/sd_income,
         income_byLog10 =log10(income))
```

]

最终得到收入的**均值变换**结果：

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]

---

### （税收案例）数据变换：收入变量的标准化变换

现在我们可以，通过如下步骤进行收入的**标准化**变换：

- 对收入进行标准化变换
`$income\_bySd  =\frac{income_i-\overline{income}}{sd\_income}$`。

]

下面展示的是用`R`计算过程：

```r
mean_income <- round(mean(training_prepared$income, na.rm = T),2)
sd_income <- round(sd(training_prepared$income, na.rm = T),2)

training_prepared <-  training_prepared %>%
  left_join(., median_income_table, by="state_of_res") %>% 
  mutate(income_byMedian = income/median_income, 
         income_byMean = income/mean_income, 
*        income_bySd = (income- mean_income)/sd_income,
         income_byLog10 =log10(income))
```

]

最终得到收入的**标准化**变换结果：

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]

---

### （税收案例）数据变换：收入变量的对数化变换

现在我们可以，通过如下步骤进行收入的**对数化**变换：

- 对收入进行**对数化**变换
`$income\_byLog10  =log_{10}^{(income_i)}$`。

]

下面展示的是用`R`计算过程：

```r
mean_income <- round(mean(training_prepared$income, na.rm = T),2)
sd_income <- round(sd(training_prepared$income, na.rm = T),2)

training_prepared <-  training_prepared %>%
  left_join(., median_income_table, by="state_of_res") %>% 
  mutate(income_byMedian = income/median_income, 
         income_byMean = income/mean_income, 
         income_bySd = (income- mean_income)/sd_income, 
*        income_byLog10 =log10(income))
```

]

最终得到收入的**对数化**变换结果：

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]

---

### （税收案例）数据变换：收入变换前后分布的比较

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-48-1.png" alt="年收入的直方图"  />
<p class="caption">年收入的直方图</p>
</div>

]

]

]

]

]

---

### （税收案例）数据变换：批量标准化处理

对于数据集的数值型变量（`age`,`income`,`num_veicles`,`gas_usage`），我们可以同时进行批量**标准化**变换。从而为下一步建模分析做准备。

如下是利用`R`软件函数`scale()`进行批量标准化处理的代码：

```r
dataf <- training_prepared[, c("age", "income", "num_vehicles", "gas_usage")]

*dataf_scaled <- scale(dataf, center=TRUE, scale=TRUE)
```

]

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---

### （税收案例）数据变换：批量变换为分类变量

我们还可以把**连续变量**年龄(`age`)，变换为**分类变量**(`age_range`和`age_cat`)。其中分割依据为`brks <- c(0, 18, 45, 65, Inf)`。

```r
*brks <- c(0, 18,45, 65, Inf)

training_prepared <- training_prepared %>%
  select(id, age) %>%
  filter(!is.na(age)) %>%
* mutate(age_range = cut(age, breaks = brks,
                         include.lowest = T),
*        age_cat = cut(age, breaks = brks,
                       include.lowest = T, labels = FALSE))
```

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]

---

### 数据子集：概念

**数据子集**（data subset）是对数据集进行抽样（sampling）的过程，形成的数据子集一般用于后续的建模分析。

- 训练集（training subset）：主要用于参数估计，得到一个最终估计模型。

- 测试集（test subset）：主要用于对估计模型的预测准确性进行评估。

---

### 数据子集：训练集和测试集

---

### （税收案例）数据子集：设置子集样本数量

对全部数据集`custom_data`（样本数n=73262），我们可以生成名为`gp`的新列，采用[0,1]的**均匀随机分布**（uniform distribution），对应的R函数为`runif(n)`

假定我们希望数据子集的容量分别为：

- **训练集**样本数
`$n_{train} =$` 90% X 73262 =65421个。

- **测试集**样本数
`$n_{test} =$` 10% X 73262 =7841个。

]

```r
set.seed(25643)
customer_data <- customer_data %>%
* mutate(gp =round(runif(nrow(.)),2))
pct <- 0.1

customer_test <- subset(customer_data, gp <= pct)
customer_train <- subset(customer_data, gp > pct)

n_all <- nrow(customer_data)
n_test <- nrow(customer_test)

n_train <- nrow(customer_train)
```

]

---

### （税收案例）数据子集：比较三个数据集

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---

### （税收案例）数据子集：等比例随机抽取

下面我们随机抽取数据集的10%作为子集，其中要求按所在州（`state_of_res`）来等比例分配：

```r
vars_sel <- c("id","state_of_res","age", "sex","income")

spl_state <- customer_data %>%
  select(one_of(vars_sel)) %>%
* group_by(state_of_res) %>%
* sample_frac(0.1) %>%
  arrange(id) 
```

]

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]

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<script type="application/json" data-for="htmlwidget-9be27ea3891ade8e541f">{"x":{"filter":"none","caption":"<caption>抽取后各州样本数量n=7325<\/caption>","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40","41","42","43","44","45","46","47","48","49","50","51"],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51],["Alabama","Alaska","Arizona","Arkansas","California","Colorado","Connecticut","Delaware","District of Columbia","Florida","Georgia","Hawaii","Idaho","Illinois","Indiana","Iowa","Kansas","Kentucky","Louisiana","Maine","Maryland","Massachusetts","Michigan","Minnesota","Mississippi","Missouri","Montana","Nebraska","Nevada","New Hampshire","New Jersey","New Mexico","New York","North Carolina","North Dakota","Ohio","Oklahoma","Oregon","Pennsylvania","Rhode Island","South Carolina","South Dakota","Tennessee","Texas","Utah","Vermont","Virginia","Washington","West Virginia","Wisconsin","Wyoming"],[105,16,153,65,896,129,83,20,17,498,220,35,33,292,147,71,65,94,110,32,134,164,227,123,67,140,22,41,67,31,206,40,443,236,17,261,90,95,300,22,118,19,150,603,66,15,194,168,42,130,13]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>index<\/th>\n      <th>state_of_res<\/th>\n      <th>n<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":5,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

]

---
layout: false
class: center, middle, duke-softblue,hide_logo
name: quality

# 3.2 品质数据的整理与展示

### 分类数据的整理与图示

### 顺序数据的整理与图示

---
layout: true

<div class="my-footer"><span>huhuaping@  &emsp;&emsp; <a href="#chapter02"> 第03章 数据的图表展示 </a>
&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;
<a href="#quality"> 3.2 品质数据的整理与展示 </a> </span></div>

---

## 分类数据：整理与图示的基本过程

- 列出各类别

- 分类数据的整理与图示

- 制作频数分布表

- 用图形显示数据

---

## 分类数据：计算统计量并制表

- 频数(frequency) ：落在各类别中的数据个数

- 比例(proportion)：某一类别数据个数占全部数据个数的比值

- 百分比(percentage) ：将对比的基数作为100而计算的比值

- 比率(ratio) ：不同类别数值个数的比值

---
exclude: true

## 案例：饮料销售

---

### （案例）饮料销售

**案例**：一家市场调查公司为研究不同品牌饮料的市场占有率，对随机抽取的一家超市进行了调查。

调查员在某天对50名顾客购买饮料的品牌进行了记录，如果一个顾客购买某一品牌的饮料，就将这一饮料的品牌名字记录一次。

]

下边就是记录的原始数据：

<div id="htmlwidget-f83f07cb805f618f03d6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-f83f07cb805f618f03d6">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40","41","42","43","44","45","46","47","48","49","50"],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50],["女","男","男","女","男","男","女","女","男","男","女","女","男","男","男","女","男","女","男","男","女","男","男","女","男","女","男","女","女","女","男","男","女","男","女","女","女","女","男","女","女","女","男","女","女","女","女","男","女","女"],["碳酸饮料","绿茶","矿泉水","矿泉水","碳酸饮料","矿泉水","碳酸饮料","绿茶","果汁","碳酸饮料","矿泉水","其他","碳酸饮料","绿茶","碳酸饮料","其他","矿泉水","碳酸饮料","绿茶","其他","碳酸饮料","绿茶","绿茶","碳酸饮料","碳酸饮料","绿茶","矿泉水","绿茶","碳酸饮料","矿泉水","其他","碳酸饮料","果汁","矿泉水","其他","碳酸饮料","其他","果汁","绿茶","果汁","碳酸饮料","果汁","矿泉水","碳酸饮料","绿茶","其他","果汁","绿茶","其他","矿泉水"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>index<\/th>\n      <th>gender<\/th>\n      <th>brand<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":6,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[6,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

]

---

### （案例）饮料销售：单变量制表（饮料类别）

根据原始数据，我们可以整理并列出所有饮料类别：

<div id="htmlwidget-ce637057fd45eff7e1d6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-ce637057fd45eff7e1d6">{"x":{"filter":"none","data":[["1","2","3","4","5"],["果汁","矿泉水","绿茶","其他","碳酸饮料"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

统计得到各饮料类别的购买人数（频次）：

<div id="htmlwidget-6b6404f9d5522709b4e6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-6b6404f9d5522709b4e6">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["果汁","矿泉水","绿茶","其他","碳酸饮料","Total"],[6,10,11,8,15,50]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>n<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

进一步统计得到各饮料类别的购买人数占比（频率）：

<div id="htmlwidget-465741e94bff6ebc90d7" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-465741e94bff6ebc90d7">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["果汁","矿泉水","绿茶","其他","碳酸饮料","Total"],[6,10,11,8,15,50],["12.0%","20.0%","22.0%","16.0%","30.0%","100.0%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

### （案例）饮料销售：双变量制表（饮料类别VS性别）

根据原始数据，我们可以对饮料类别和性别进行交叉分组：

<div id="htmlwidget-6ff126c0ad7477a5f447" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-6ff126c0ad7477a5f447">{"x":{"filter":"none","data":[["1","2","3","4","5"],["果汁","矿泉水","绿茶","其他","碳酸饮料"],[null,null,null,null,null],[null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>男<\/th>\n      <th>女<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

统计得到交叉分组下的购买人数（频次）：

<div id="htmlwidget-cd231ae4107b96ca9dc8" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-cd231ae4107b96ca9dc8">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["果汁","矿泉水","绿茶","其他","碳酸饮料","Total"],[1,6,7,2,6,22],[5,4,4,6,9,28],[6,10,11,8,15,50]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>男<\/th>\n      <th>女<\/th>\n      <th>Total<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

进一步统计得到交叉分组下购买人数占比（频率）及其**列合计**：

<div id="htmlwidget-af9a855d63e818336215" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-af9a855d63e818336215">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["果汁","矿泉水","绿茶","其他","碳酸饮料","Total"],["4.5%","27.3%","31.8%","9.1%","27.3%","100.0%"],["17.9%","14.3%","14.3%","21.4%","32.1%","100.0%"],["12.0%","20.0%","22.0%","16.0%","30.0%","100.0%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>男<\/th>\n      <th>女<\/th>\n      <th>Total<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

同时，也可统计得到交叉分组下购买人数占比（频率）及其**行合计**：

<div id="htmlwidget-50ebf3cb2f0665ab472e" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-50ebf3cb2f0665ab472e">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["果汁","矿泉水","绿茶","其他","碳酸饮料","Total"],["16.7%","60.0%","63.6%","25.0%","40.0%","44.0%"],["83.3%","40.0%","36.4%","75.0%","60.0%","56.0%"],["100.0%","100.0%","100.0%","100.0%","100.0%","100.0%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>男<\/th>\n      <th>女<\/th>\n      <th>Total<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

最后，还可以同时统计交叉分组的人数和占比（列合计）：

<div id="htmlwidget-9c3cc590df30c8c359ad" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-9c3cc590df30c8c359ad">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["果汁","矿泉水","绿茶","其他","碳酸饮料","Total"],["4.5%  (1)","27.3%  (6)","31.8%  (7)","9.1%  (2)","27.3%  (6)","100.0% (22)"],["17.9%  (5)","14.3%  (4)","14.3%  (4)","21.4%  (6)","32.1%  (9)","100.0% (28)"],["12.0%  (6)","20.0% (10)","22.0% (11)","16.0%  (8)","30.0% (15)","100.0% (50)"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>brand<\/th>\n      <th>男<\/th>\n      <th>女<\/th>\n      <th>Total<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

## 分类数据：统计制图1（条形/柱状图）

**条形/柱状图**：用宽度相同的条形的高度或长短来表示各类别数据的图形。

- 各类别可以放在纵轴，称为**条形图**(bar Chart)

- 各类别也可以放在横轴，称为**柱形图**(column chart)

**作用**：主要用于反映分类数据的频数分布。

**形式**：单式条形图/复式条形图。

---

### （案例）饮料销售：单变量柱状图/条形图

根据饮料类型购买次数的数据表，我们可以绘制出如下**柱状图**：

]

---

### （案例）饮料销售：单变量柱状图/条形图

#### b.条形图
]

根据饮料类型购买次数的数据表，还可以绘制出如下**条形图**：

]

---

### （案例）饮料销售：多变量柱状图/条形图

根据饮料类型（brand）和性别（gender）交叉分组下的购买次数表，可以绘制出如下**柱状图**：

]

---

### （案例）饮料销售：多变量柱状图/条形图

#### b.双变量条形图
]

根据饮料类型（brand）和性别（gender）交叉分组下的购买次数表，可以绘制出如下**条形图**：

]

---

## 分类数据：统计制图1（条形/柱状图）

思考：什么时候适合使用柱状图？什么时候适合使用条形图？

<div class="notes">
<p>待完成：找到新数据，绘制一张条形图，但其不适合制作柱状图。</p>
</div>

---

## 分类数据：统计制图2（饼图）

**饼图**（pie Chart）：也称圆形图，是用圆形及圆内扇形的角度来表示数值大小的图形。

**用途**：用于表示样本或总体中各组成部分所占的比例，用于研究结构性问题。

**绘制要点**：

- 样本或总体中各部分所占的频次/百分比用圆内的各个扇形角度表示。

- 扇形块的中心角度，进行**极坐标变换**（按各部分数据占比乘以3600确定）。

- 排列顺序、标签值显示。

---

### （案例）饮料销售：绘制饼图（频次1）

根据分配数据表，我们可以绘制出如下**次数**饼图：

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-83-1.png" alt="图a.饮料销售量分布（有图例）"  />
<p class="caption">图a.饮料销售量分布（有图例）</p>
</div>

]

---

### （案例）饮料销售：绘制饼图（频次2）

#### b.次数饼图2

]

可以进一步调整**次数**饼图的图例和标签数值显示：

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-84-1.png" alt="图b.饮料销售量分布（无图例）"  />
<p class="caption">图b.饮料销售量分布（无图例）</p>
</div>

]

---

### （案例）饮料销售：绘制饼图（占比）

#### b.次数饼图2

#### c.占比饼图1

]

可以进一步调整**占比**饼图的图例和标签数值显示：

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-85-1.png" alt="图c.饮料销售占比（有图例）"  />
<p class="caption">图c.饮料销售占比（有图例）</p>
</div>

]

---

### （案例）饮料销售：绘制饼图（占比2）

#### b.次数饼图2

#### c.占比饼图1

#### d.占比饼图2

]

根据分配数据表，我们可以绘制出如下**次数**饼图：

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-86-1.png" alt="图d.饮料销售占比（无图例）"  />
<p class="caption">图d.饮料销售占比（无图例）</p>
</div>

]

---

## 顺序数据：统计量和图表

对于顺序型分组（上小下大）数据，主要的统计指标包括：

- **累积频数**（cumulative frequencies）：各类别频数的逐级累加。

- **累积频率**（cumulative percentages）：各类别频率(百分比)的逐级累加。

对于以上累积统计指标，又分别包括：

- **较小制累积**（频数/频率）：又称为向上累积或以下累积，本组及以下次数/频率的逐级累加。

- **较大制累积**（频数/频率）：又称为向下累积或以上累积，本组及以上次数/频率的逐级累加。

制表和绘图分别有：

- 累积频数/频率表等

- 累积频数/频率图、环形图等

---

### （案例）住房满意度：原始数据

```
Warning in rep(c("甲城市", "乙城市"), each = c(sum(reps),
sum(reps2))): 只用'each'参数里的第一个元素
```

---

### （案例）住房满意度：案例数据

**案例说明**：在一项城市住房满意度问题的研究中，研究人员在甲城市抽样调查300家庭户，其中的一个问题是：

```
您对您家庭目前的住房状况是否满意？

1.非常不满意；2.不满意；3.一般；4.满意；5.非常满意

```

]

下边就是收集到的不同满意度评价水平的频次和频率数据表：

<div id="htmlwidget-0bb1855e6858dc52b012" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-0bb1855e6858dc52b012">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["A","B","C","D","E","-"],["非常不满意","不满意","一般","满意","非常满意","Total"],[24,108,93,45,30,300],["8.0%","36.0%","31.0%","15.0%","10.0%","100.0%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>satisfication<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

]

---

### （案例）住房满意度：计算统计量并制表

我们可以计算得到**较小制**下的累积频次和频率，并制表：

<div id="htmlwidget-f28dc336cde7ef50bfb6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-f28dc336cde7ef50bfb6">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["A","B","C","D","E","-"],["非常不满意","不满意","一般","满意","非常满意","Total"],[24,108,93,45,30,300],["8.0%","36.0%","31.0%","15.0%","10.0%","100.0%"],["24","132","225","270","300","-"],["8.0%","44.0%","75.0%","90.0%","100.0%","-"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>satisfication<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n      <th>min_cum_n<\/th>\n      <th>min_cum_p<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

我们也可以计算得到**较大制**下的累积频次和频率，并制表：

<div id="htmlwidget-890dcd52065cfc97704d" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-890dcd52065cfc97704d">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["A","B","C","D","E","-"],["非常不满意","不满意","一般","满意","非常满意","Total"],[24,108,93,45,30,300],["8.0%","36.0%","31.0%","15.0%","10.0%","100.0%"],["300","276","168","75","30","-"],["100.0%","92.0%","56.0%","25.0%","10.0%","-"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>satisfication<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n      <th>max_cum_n<\/th>\n      <th>max_cum_p<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

我们可以对比观测**较小制**和**较大制**下的累积频次和频率：

<div id="htmlwidget-ec2d089525a181e722f8" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-ec2d089525a181e722f8">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["A","B","C","D","E","-"],["非常不满意","不满意","一般","满意","非常满意","Total"],[24,108,93,45,30,300],["8.0%","36.0%","31.0%","15.0%","10.0%","100.0%"],["24","132","225","270","300","-"],["8.0%","44.0%","75.0%","90.0%","100.0%","-"],["300","276","168","75","30","-"],["100.0%","92.0%","56.0%","25.0%","10.0%","-"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>satisfication<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n      <th>min_cum_n<\/th>\n      <th>min_cum_p<\/th>\n      <th>max_cum_n<\/th>\n      <th>max_cum_p<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

]

---

### （案例）住房满意度：绘制累计频次/频率图

]

]

]

]

---
exclude: true

### my ggplot theme

参考：

- [Changing fonts in ggplot2](https://stackoverflow.com/questions/34522732/changing-fonts-in-ggplot2)

- `extrafont` pkg [on github](https://github.com/wch/extrafont)

---
exclude: true

### test chart

---

### （案例）住房满意度：绘制环形图

**环形图**(doughnut chart)：环形图中间有一个“空洞”，样本或总体中的每一部分数据用环中的一段表示。

**用途**：用于结构比较研究；用于展示分类和顺序数据。

与饼图的联系与区别：

- 饼图只能显示一个总体各部分所占的比例。

- 环形图则可以同时绘制多个样本或总体的数据系列，每一个样本或总体的数据系列为一个环。

---

### （案例）住房满意度：绘制环形图

**案例说明**：继续前述甲城市满意度的研究，为了综合比较城市家庭满意度。研究者继续收集并获得了乙城市家庭的满意度评价数据。甲乙两个城市的家庭住户满意度数据如下表所示：

<div id="htmlwidget-58a222b91926d3253022" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-58a222b91926d3253022">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10"],["甲城市","甲城市","甲城市","甲城市","甲城市","乙城市","乙城市","乙城市","乙城市","乙城市"],["非常不满意","不满意","一般","满意","非常满意","非常不满意","不满意","一般","满意","非常满意"],[24,108,93,45,30,21,99,78,64,38],["8.0%","36.0%","31.0%","15.0%","10.0%","7.0%","33.0%","26.0%","21.3%","12.7%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>city<\/th>\n      <th>satisfication<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":"5","order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":["10","100","25","5","50"]}},"evals":[],"jsHooks":[]}</script>

]

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-102-1.png" alt="图a.甲城市评价分布" height="90%" />
<p class="caption">图a.甲城市评价分布</p>
</div>

]

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-103-1.png" alt="图b.乙城市评价分布" height="90%" />
<p class="caption">图b.乙城市评价分布</p>
</div>

]

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-104-1.png" alt="图c.两个城市评价分布对比" height="90%" />
<p class="caption">图c.两个城市评价分布对比</p>
</div>

]

???

绘图参考：

- [Creating a multiple pie/donut chart](https://biostats.w.uib.no/creating-a-multiple-pie-donut-chart/)

---
layout: false
class: center, middle, duke-softblue ,hide_logo
name: quantity

# 3.3 数值型数据的整理与展示

### 数据分组的图表展示

### 数据未分组的图表展示

### 统计报表的设计

---
layout: true

<div class="my-footer"><span>huhuaping@  &emsp;&emsp; <a href="#chapter02"> 第03章 数据的图表展示 </a>
&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;
<a href="#quantity"> 3.3 数值型数据的整理与展示 </a> </span></div>

---

## 数据分组：概念和作用

**数据分组**：把同质总体中的具有不同特点的单位分开，从而正确地认识事物的本质及其规律性。

**数据分组的作用**：

- 类型分组：揭露社会经济现象的类型，反映各类型的特点。

- 结构分组：说明社会经济现象的内部结构。

- 分析分组：研究经济现象之间的依存关系。

---

## 数据分组：选择分组标志

选择分组标志的**原则**：

- 科学性

- 完备性

- 互斥性

选择分组标志的**方法**：

- 根据研究问题的目的来选择。

- 要选择最能反映被研究现象本质特征的标志。

- 要结合现象所处的具体历史条件或经济条件来选择。

---

## 数据分组：数据分组类型

**A.按分组标志的特征分**：

- 品质标志分组：反映事物属性差异

- 简单分组：如人口按性别分组。
    - 复杂分组：如人口按职业分组。

- 数量标志分组：反映事物数量差异

- 单项式数量分组：运用于变量变动幅度小、项目少的分组。
    - 组距式分组：运用于变量变动幅度大、项目多的分组。

**B.按总体所选择标志的个数分**：

- 单一分组：按一个标志对总体进行分组。

- 复合分组：按两个或两个以上标志对同一总体进行分组。

---
exclude: true

## 案例：多种分组

---

### （示例）数据分组类型：按标志特征分组1

<div id="htmlwidget-1c8857aa3ff6ef289dd7" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-1c8857aa3ff6ef289dd7">{"x":{"filter":"none","data":[["1","2"],["男","女"],[null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>性别<\/th>\n      <th>人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

<div id="htmlwidget-1606246f10b0d0c73109" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-1606246f10b0d0c73109">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12"],["急诊科医师","乡村医师","急诊护士","手术室护士","护理员","放射线之技术人员","配膳员","卫生检查员","医用气体工","医院炊事","医院勤杂工","清洁工"],[null,null,null,null,null,null,null,null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>职业<\/th>\n      <th>人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":6,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[6,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

]

---

### （示例）数据分组类型：按标志特征分组2

<div id="htmlwidget-f0cd005e3ece41fe9ec6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-f0cd005e3ece41fe9ec6">{"x":{"filter":"none","data":[["1","2","3","4","5"],[12,13,15,16,20],[null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>日产量<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

<div id="htmlwidget-6a44338c0198aef5f8a9" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-6a44338c0198aef5f8a9">{"x":{"filter":"none","data":[["1","2","3","4","5"],["18岁以下","19-25岁","26-35岁","36-45岁","45岁以上"],[null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>年龄<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

### （示例）数据分组类型：按标志个数分组

.fl.w-third.pa2[
<div id="htmlwidget-b2ab74216ab2d5ad39c6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-b2ab74216ab2d5ad39c6">{"x":{"filter":"none","data":[["1","2"],["男","女"],[null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>性别<\/th>\n      <th>人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

.fl.w-third.pa2[
<div id="htmlwidget-ccc533be37232b20e50e" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-ccc533be37232b20e50e">{"x":{"filter":"none","data":[["1","2","3","4","5"],[12,13,15,16,20],[null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>日产量<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

.fl.w-third.pa2[
<div id="htmlwidget-ea600c534e0d5ffaad87" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-ea600c534e0d5ffaad87">{"x":{"filter":"none","data":[["1","2","3","4","5"],["18岁以下","19-25岁","26-35岁","36-45岁","45岁以上"],[null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>年龄<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

]

<div id="htmlwidget-385e5146a7c34170208c" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-385e5146a7c34170208c">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8"],["理科生","理科生","理科生","理科生","文科生","文科生","文科生","文科生"],["本科生","专科生","本科生","专科生","本科生","专科生","本科生","专科生"],["男生","男生","女生","女生","男生","男生","女生","女生"],[null,null,null,null,null,null,null,null]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>学科<\/th>\n      <th>学历<\/th>\n      <th>性别<\/th>\n      <th>人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

## 分配数列：概念和类型

**分配数列**：统计总体按照某一标志分组以后，用以反映总体各单位分配情况的统计数列，称为分配数列，又可称次数分配或次数分布。

- **品质型分配数列**。

- **数值型分配数列**。根据分组情况，具体又分为：

- **单项变量数列**：按每个变量值分别列组编制数列。适用于不连续变量或变量能以整数表示，其变动范围不大时。 
    - **组距变量数列**：按组距分组编制数列。适用于连续变量或变量可用小数表示，其变动范围。

---

### （示例）分配数列的类型：数值型分配数列

<div id="htmlwidget-28a16bd2eade430a480f" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-28a16bd2eade430a480f">{"x":{"filter":"none","data":[["1","2","3","4","5"],[12,13,15,16,20],[109,136,144,107,124]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>日产量<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

<div id="htmlwidget-767c76029fc97e0e8a14" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-767c76029fc97e0e8a14">{"x":{"filter":"none","data":[["1","2","3","4","5"],["18岁以下","19-25岁","26-35岁","36-45岁","45岁以上"],[1117,903,1113,883,860]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>年龄<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

## 组距式数据分组：类型

根据分组是否开口以及是否等距，组距式分配数列可以分为如下类型：

- 按两端组是否开口分：

- **开口式分组**：最小组与最大组不封口。

- **闭口式分组**：所有组都有明确上限和下限。

- 按组距是否为等距分：

- **等距式分组**：所有分组的组距全部相等。

- **异距式分组**：各个分组组距不是完全相等。

---

### （示例）组距式分配数列的类型

<div id="htmlwidget-7ec54f896c7d36503c43" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-7ec54f896c7d36503c43">{"x":{"filter":"none","data":[["1","2","3","4","5"],["50-60","60-70","70-80","80-90","90-100"],[2,7,11,12,8]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>成绩<\/th>\n      <th>人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

<div id="htmlwidget-bc5f25103ba1c6c08921" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-bc5f25103ba1c6c08921">{"x":{"filter":"none","data":[["1","2","3","4","5"],["18岁以下","19-25岁","26-35岁","36-45岁","45岁以上"],[1117,903,1113,883,860]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>年龄<\/th>\n      <th>职工人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

## 组距式数据分组：重要概念

关于组距式分配数列，我们需要掌握如下重要概念：

- **组数（bins）**：数据分组的总组数。

- **组限（limits）**：组距两端的数值。分为上限和下限。

a. **下限(lower limit)** ：一个组的最小值。
    
    b. **上限(upper limit)** ：一个组的最大值。

- **组距（width）** ：某组的上限与下限之差。

- **组中值(class midpoint) **：某组的下限与上限之间的中点值

- **全距（range）**：整个分组数列中，最大组**上限**与最小组**下限**之差。

- **最大组/最小组**：整个分组数列中，分组标志数值最大/最小的那一组。

---

## 组距式数据分组：分组步骤

组距式数据分组的主要步骤包括：

- 确定组数：组数的确定应以能够显示数据的分布特征和规律为目的。在实际分组时，组数一般为
`$5\leq K \leq 15$`。

- 确定组距：组距是一个组的上限与下限之差，可根据全部数据的最大值和最小值及所分的组数来确定。例如，
`$组距＝\frac{(最大值 - 最小值)}{组数}$`

- 确定组限。对于连续变量分组，各组之间的组限也要连续。对于不连续变量分组，组与组之间的组限往往是间断的。此外，在同一个组距数列中，组限标准保持一致。

- 统计出各组的频数并整理成频数分布表。在登记次数时，应遵守：

- 上组限不在内：适用于越大越好的变量，如产值。
    - 下组限不在内：适用于越小越好的变量，如成本。

---

## 组距式数据分组：组中值的计算

组中值的计算，需要考虑分组是否开口：

- 闭口式分组的组中值求法：

`$$\begin{align}
\text{组中值} = \frac{\text{组上限}+\text{组下限}}{2}
&= 组下限 + \frac{\text{组上限}-\text{组下限}}{2} \\
&= 组上限 - \frac{\text{组上限}-\text{组下限}}{2} 
\end{align}$$`

- 开口式分组的组中值求法：

`$$\begin{align}
\text{下开口组的组中值} &= 组上限 - \frac{\text{邻组组距}}{2}\\
\text{上开口组的组中值} &= 组下限 + \frac{\text{邻组组距}}{2}
\end{align}$$`

---
exclude:true

## （案例）学生考试成绩

---

### （案例）学生考试成绩：原始数据

**案例说明**：某班级共有40名学生，在《统计学原理》课程考试中成绩如下：

```
s01 s02 s03 s04 s05 s06 s07 s08 s09 s10 s11 s12 s13 s14 s15 s16 s17 
 63  88  72  69  80  80  61  68  79  81  76  76  77  78  90  89  61 
s18 s19 s20 s21 s22 s23 s24 s25 s26 s27 s28 s29 s30 s31 s32 s33 s34 
 84  92  67  65  57  62  60  66  87  80  92  78  86  71  71  63  74 
s35 s36 s37 s38 s39 s40 
 67  70  91  64  79  65 
```

---

### （案例）学生考试成绩：组距式分组操作1

假定采用**等距-闭口**分组方法，且设定分组数量为5，组距为10。

利用原始数据，进行分组得到如下结果：

<div id="htmlwidget-e6a8d288941eb9fc458c" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-e6a8d288941eb9fc458c">{"x":{"filter":"none","data":[["1","2","3","4","5"],["(50,60⦌","(60,70⦌","(70,80⦌","(80,90⦌","(90,100⦌"],["(s22)57;  (s24)60","(s01)63;  (s04)69;  (s07)61;  (s08)68;  (s17)61;  (s20)67;  (s21)65;  (s23)62;  (s25)66;  (s33)63;  (s35)67;  (s36)70;  (s38)64;  (s40)65","(s03)72;  (s05)80;  (s06)80;  (s09)79;  (s11)76;  (s12)76;  (s13)77;  (s14)78;  (s27)80;  (s29)78;  (s31)71;  (s32)71;  (s34)74;  (s39)79","(s02)88;  (s10)81;  (s15)90;  (s16)89;  (s18)84;  (s26)87;  (s30)86","(s19)92;  (s28)92;  (s37)91"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>成绩分组<\/th>\n      <th>学生成绩<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

---

### （案例）学生考试成绩：组距式分组操作2

以前述**考试成绩**案例分组数据为例，相关概念包括（见下表）：

- **组数（bins）**为5

- **组距（width）** 为10

- **全距（range）**为50（注意原始数据的全距）

- 最小组和最大组分别为第1组和第5组

- 下限、上限、组距和组中值分别见右表

]

**分组数据表**：

<div id="htmlwidget-66bbbffa6708a6ce1a01" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-66bbbffa6708a6ce1a01">{"x":{"filter":"none","data":[["1","2","3","4","5"],["(50,60⦌","(60,70⦌","(70,80⦌","(80,90⦌","(90,100⦌"],[2,14,14,7,3],[50,60,70,80,90],[60,70,80,90,100],[10,10,10,10,10],[55,65,75,85,95]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>成绩分组<\/th>\n      <th>人数<\/th>\n      <th>下限<\/th>\n      <th>上限<\/th>\n      <th>组距<\/th>\n      <th>组中组<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---

## 组距式数据分组：异矩情形

在**异矩分组**下，我们需要进一步计算各组的**组密度**以及**标准组距分布**：

`$$\begin{align}
\text{次数密度} &= \frac{\text{各组次数}}{各组组距}\\
\text{频率密度} &= \frac{\text{各组频率}}{各组组距}
\end{align}$$`

`$$\begin{align}
\text{标准组距次数分布} &= \frac{\text{各组次数}}{标准化组距}\\
\text{标准组距频率分布} &= \frac{\text{各组频率}}{标准化组距}
\end{align}$$`

---
exclude: true

### （案例）学生考试成绩：异矩分组

---

### （案例）学生考试成绩：异矩分组情形

继续前述**考试成绩**案例，如果分组时不小心处理成了如下异矩分组：

<div id="htmlwidget-b92760ad8db823f34477" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-b92760ad8db823f34477">{"x":{"filter":"none","data":[["1","2","3","4"],["(50,60⦌","(60,80⦌","(80,90⦌","(90,100⦌"],[2,28,7,3],[50,60,80,90],[60,80,90,100],[10,20,10,10],[55,70,85,95]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>成绩分组<\/th>\n      <th>人数<\/th>\n      <th>下限<\/th>\n      <th>上限<\/th>\n      <th>组距<\/th>\n      <th>组中组<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

---

### （案例）学生考试成绩：异矩分组统计量

在异矩分组情形下，**频次密度**和**标准组距频次**计算如下：

<div id="htmlwidget-9c21894a155ca85239b1" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-9c21894a155ca85239b1">{"x":{"filter":"none","data":[["1","2","3","4"],["(50,60⦌","(60,80⦌","(80,90⦌","(90,100⦌"],[2,28,7,3],[50,60,80,90],[60,80,90,100],[10,20,10,10],[55,70,85,95],[0.2,1.4,0.7,0.3],[2,14,7,3]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>成绩分组<\/th>\n      <th>人数<\/th>\n      <th>下限<\/th>\n      <th>上限<\/th>\n      <th>组距<\/th>\n      <th>组中组<\/th>\n      <th>频次密度<\/th>\n      <th>标准组距人数<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

---

## 数据分组：统计制表（类型）

对分组数据进行统计制表，也即用统计表来表示次数/频率等统计量在各组的分布情况，主要包括。

- **频数表**/**百分数表**（已经展示，见前面slide）

]

**累计次数表**/**累计百分数表**。复习之前的定义，具体为：

- 较小制累计（以下累计、向上累计）：即（上限）以下累计次数，每一组的累计次数表示小于该组上限（变量）值的次数/频率共有多少。

- 较大制累计（以上累计、向下累计）：即（下限）以上累计次数：每一组的累计次数表示大于该组下限（变量）值的次数/频率共有多少。

]

**交叉分析表**，又称为**交叉列联表**（cross-table），是对复合式分组数列的频数或频率统计，便于对两个或多个分组标志（分组变量）关系的直接观察。

数据交叉形式可以是：

- 品质变量VS品质变量

- 品质变量VS数值变量（较少用*）

- 数值变量VS数值变量（较少用*）

]

---

### （案例）学生考试成绩：累积次数/频率表

对于等距式分组情形，我们可以分别计算出较小/较大累计次数/频率：

我们可以计算得到**较小制**下的累积频次和频率，并制表：

<div id="htmlwidget-475a370613ef66e018e7" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-475a370613ef66e018e7">{"x":{"filter":"none","data":[["1","2","3","4","5"],["(50,60⦌","(60,70⦌","(70,80⦌","(80,90⦌","(90,100⦌"],[2,14,14,7,3],["5.0%","35.0%","35.0%","17.5%","7.5%"],[2,16,30,37,40],["5.0%","40.0%","75.0%","92.5%","100.0%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n      <th>min_cum_n<\/th>\n      <th>min_cum_p<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

我们也可以计算得到**较大制**下的累积频次和频率，并制表：

<div id="htmlwidget-48728308d3aac6b7abf6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-48728308d3aac6b7abf6">{"x":{"filter":"none","data":[["1","2","3","4","5"],["(50,60⦌","(60,70⦌","(70,80⦌","(80,90⦌","(90,100⦌"],[2,14,14,7,3],["5.0%","35.0%","35.0%","17.5%","7.5%"],[40,38,24,10,3],["100.0%","95.0%","60.0%","25.0%","7.5%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n      <th>max_cum_n<\/th>\n      <th>max_cum_p<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

我们可以对比观测**较小制**和**较大制**下的累积频次和频率：

<div id="htmlwidget-ad6796e20ae4653063c3" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-ad6796e20ae4653063c3">{"x":{"filter":"none","data":[["1","2","3","4","5"],["(50,60⦌","(60,70⦌","(70,80⦌","(80,90⦌","(90,100⦌"],[2,14,14,7,3],["5.0%","35.0%","35.0%","17.5%","7.5%"],[2,16,30,37,40],["5.0%","40.0%","75.0%","92.5%","100.0%"],[40,38,24,10,3],["100.0%","95.0%","60.0%","25.0%","7.5%"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>groups<\/th>\n      <th>n<\/th>\n      <th>percent<\/th>\n      <th>min_cum_n<\/th>\n      <th>min_cum_p<\/th>\n      <th>max_cum_n<\/th>\n      <th>max_cum_p<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"scrollX":true,"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>
]

]

---

### （案例）学生考试成绩：等距分组的交叉分析表

对于前述**学生考试成绩**案例，研究者还收集了40名学生的性别信息（见下表）。

<div id="htmlwidget-31e5ccfbfaf0aaf0f057" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-31e5ccfbfaf0aaf0f057">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40"],["s01","s02","s03","s04","s05","s06","s07","s08","s09","s10","s11","s12","s13","s14","s15","s16","s17","s18","s19","s20","s21","s22","s23","s24","s25","s26","s27","s28","s29","s30","s31","s32","s33","s34","s35","s36","s37","s38","s39","s40"],[63,88,72,69,80,80,61,68,79,81,76,76,77,78,90,89,61,84,92,67,65,57,62,60,66,87,80,92,78,86,71,71,63,74,67,70,91,64,79,65],["女生","男生","女生","女生","男生","女生","男生","女生","女生","女生","男生","男生","女生","男生","男生","女生","女生","女生","男生","男生","女生","女生","女生","女生","女生","男生","女生","女生","男生","男生","女生","女生","男生","男生","男生","女生","女生","女生","女生","男生"],["(60,70⦌","(80,90⦌","(70,80⦌","(60,70⦌","(70,80⦌","(70,80⦌","(60,70⦌","(60,70⦌","(70,80⦌","(80,90⦌","(70,80⦌","(70,80⦌","(70,80⦌","(70,80⦌","(80,90⦌","(80,90⦌","(60,70⦌","(80,90⦌","(90,100⦌","(60,70⦌","(60,70⦌","(50,60⦌","(60,70⦌","(50,60⦌","(60,70⦌","(80,90⦌","(70,80⦌","(90,100⦌","(70,80⦌","(80,90⦌","(70,80⦌","(70,80⦌","(60,70⦌","(70,80⦌","(60,70⦌","(60,70⦌","(90,100⦌","(60,70⦌","(70,80⦌","(60,70⦌"]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>ID<\/th>\n      <th>score<\/th>\n      <th>gender<\/th>\n      <th>groups<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":"6","order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":["10","100","25","50","6"]}},"evals":[],"jsHooks":[]}</script>

]

此时，可以根据需要绘制出性别变量与成绩分组的**交叉分析表**（列联表）：

<div id="htmlwidget-879bd19947c1a07289ea" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-879bd19947c1a07289ea">{"x":{"filter":"none","data":[["1","2","3","4","5","6"],["(50,60⦌","(60,70⦌","(70,80⦌","(80,90⦌","(90,100⦌","Total"],[0,5,6,4,1,16],[2,9,8,3,2,24],[2,14,14,7,3,40]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>成绩分组<\/th>\n      <th>男生<\/th>\n      <th>女生<\/th>\n      <th>Total<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":[],"jsHooks":[]}</script>

]

---
exclude: true

### （示例）普森悖论交叉表

**普森悖论**（Simpson's paradox）：在有些情形中，依据从综合的交叉列联表中得出的结论可能与依据未综合数据得出的结论截然相反。这一现象就是著名的辛普森悖论。

<div class="notes">
<p>待完成：</p>
<p>case of Verdict between Kendall and Luckett. <a href="https://www.britannica.com/topic/Simpsons-paradox">see link</a></p>
<p>Simpson’s Paradox: Two HR examples with R code. <a href="https://paulvanderlaken.com/2017/09/27/simpsons-paradox-two-hr-examples-with-r-code/">see link</a></p>
</div>

---

## 数据分组：统计制图

分组数列的图示方法，也即用统计图形来表示频数/频率在各组的分布情况，主要包括的图形类型有：

a. **条形/柱状图**[已讲，见前面slide]

b. **折线图**（line chart）

c. **累积频次/频率图**（cumulative chart）

---

### （案例）学生考试成绩：绘制柱状图/折线图

]

]

---

### （案例）学生考试成绩：绘制累计频次/频率图

]

]

]

]

---

## 数据未分组：统计制图1（茎叶图）

**茎叶图（stem and leaf diagrams）**：用于显示未分组的原始数据的分布。
由“茎”和“叶”两部分构成，其图形是由数字组成的，以该组数据的高位数值作树茎，低位数字作树叶，树叶上只保留最后一位数字。

茎叶图与**横直方图**的区别*：

- 直方图可观察一组数据的分布状况，但没有给出具体的数值。

- 茎叶图既能给出数据的分布状况，又能给出每一个原始数值，保留了原始数据的信息。

- 直方图适用于大批量数据，茎叶图适用于小批量数据。

.footnote[注释：\* 茎叶图曾经的优势（简单、可手工绘制）在今天这个计算机时代也显得并不突出，因此，除非特殊情况，建议主要使用直方图作为密度函数估计工具。[see link](https://msg-book.netlify.app/gallery.html#section-11)]

---

### （案例）学生考试成绩：绘制茎叶图

继续考虑之前的**学生考试成绩案例**。40名学生课程考试成绩如下：

]

```
s22 s24 s07 s17 s23 s01 s33 s38 s21 s40 s25 s20 s35 s08 s04 s36 s31 
 57  60  61  61  62  63  63  64  65  65  66  67  67  68  69  70  71 
s32 s03 s34 s11 s12 s13 s14 s29 s09 s39 s05 s06 s27 s10 s18 s30 s26 
 71  72  74  76  76  77  78  78  79  79  80  80  80  81  84  86  87 
s02 s16 s15 s37 s19 s28 
 88  89  90  91  92  92 
```

]

```

The decimal point is 1 digit(s) to the right of the |

5 | 7
  6 | 01123345567789
  7 | 011246678899
  8 | 000146789
  9 | 0122
```

]

???

<div class="notes">
<p>待完成：提供示例数据，并绘制茎叶图。</p>
<p>Basic R Guide for NSC Statistics. <a href="https://bookdown.org/dli/rguide/stem-and-leaf-plot.html">see link</a></p>
<p>R – Stem and Leaf Plots. <a href="https://www.geeksforgeeks.org/r-stem-and-leaf-plots/">see link</a></p>
</div>

---

## 数据未分组：统计制图2（箱线图）

**箱线图（box plot）**：用于显示未分组的原始数据的分布。由一组数据的5个特征值绘制而成，它由一个箱子和两条线段组成。箱线图也被称为Median/Quartile/Range箱线图。

绘制方法：

- 首先找出一组数据的5个特征值，即最大值（Max）、最小值（Min）、中位数
`$M_e$`和两个四分位数（下四分位数
`$Q_L$`和上四分位数
`$Q_U$`）。

- 连接两个四分位数画出箱子，再将两个极值点与箱子相连接。

图形分类：

- 单一箱线图

- 多批箱线图

---

### （案例）学生考试成绩：绘制单一箱线图

继续考虑之前的**学生考试成绩案例**。40名学生课程考试成绩如下：

]

- 中位数
`$median = 75$`

- 极大值
`$median = 92$`

- 极小值
`$median = 57$`

- 四分之一位数
`$median = 65.75$`

- 四分之三位数
`$median = 80.25$`

]

]

---

### （案例）学生考试成绩：绘制多批箱线图

同时考虑学生性别和**考试成绩**。40名学生课程考试信息如下：

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]

---

## 数据未分组：统计制图3（直方图）

**直方图（histogram）**：用于展示分组数据分布的一种图形，用矩形的宽度和高度来表示频数分布。

- 本质上是用矩形的面积来表示频数分布。

- 在直角坐标中，用横轴表示数据分组，纵轴表示频数或频率，各组与相应的频数就形成了一个矩形。

直方图与柱状图的区别：

- 柱状图是用柱形的高度表示各类别频数的多少，其宽度（表示类别）则是固定的。

- 直方图是用面积表示各组频数的多少，矩形的高度表示每一组的频数或百分比，宽度则表示各组的组距，其高度与宽度均有意义。

- 直方图的各矩形通常是连续排列，柱状图则是分开排列。

- 柱状图主要用于展示分类/分组数据，直方图则主要用于展示数值型数据。

---
exclude: true

## （案例）学生考试成绩：补充数据

---

### （示例）数据未分组的制图：直方图（histogram）

**案例说明**：某个学院共有2000名学生参加《统计学原理》课程考试，考试成绩和性别信息如下：

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class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>ID<\/th>\n      <th>gender<\/th>\n      <th>score<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":5,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

]

<div id="htmlwidget-657abb7f9bba5217a0e0" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-657abb7f9bba5217a0e0">{"x":{"filter":"none","caption":"<caption>全样本概览<\/caption>","data":[["1"],["score"],[2000],[83.4605],[82],[100],[69]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>variables<\/th>\n      <th>n<\/th>\n      <th>mean<\/th>\n      <th>median<\/th>\n      <th>max<\/th>\n      <th>min<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"targets":3,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n  }"},{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":["options.columnDefs.0.render"],"jsHooks":[]}</script>

我们再按性别分两类样本数据来看成绩情况：

<div id="htmlwidget-71f0d588919ef55c7202" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-71f0d588919ef55c7202">{"x":{"filter":"none","caption":"<caption>性别子集概览<\/caption>","data":[["1","2"],["男生组","女生组"],["score","score"],[800,1200],[85.4325,82.1458333333333],[85.5,81],[100,98],[70,69]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>set<\/th>\n      <th>variables<\/th>\n      <th>n<\/th>\n      <th>mean<\/th>\n      <th>median<\/th>\n      <th>max<\/th>\n      <th>min<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"t","columnDefs":[{"targets":4,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n  }"},{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"order":[],"autoWidth":false,"orderClasses":false}},"evals":["options.columnDefs.0.render"],"jsHooks":[]}</script>

]

]

]

---

## 数据未分组：统计制图4（线图）

**线图(line plot)**：主要用于表示时间序列数据趋势的图形。

绘制要点：

- 时间一般绘在横轴，数据绘在纵轴。

- 图形的长宽比例大致为`10:7`。

- 一般情况下，纵轴数据下端应从“0”开始，以便于比较。数据与“0”之间的间距过大时，可以采取折断的符号将纵轴折断。

---
exclude: true

## （案例）新冠疫情

---
class: DT

### （案例）全球新冠疫情：数据说明

**案例说明**：研究人员收集了8个国家（US、France、Norway、Switzerland、United Kingdom、Germany、Italy、Spain），共3260条新冠疫情数据（见下表）。

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---

### （案例）全球新冠疫情：死亡率线图

为了比较各国新冠死亡率的变化趋势，绘制得到如下线图：

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## 数据未分组：统计制图5（散点图）

**散点图（Scatter plots）**：展示**两个变量**之间的关系。

用横轴代表变量
`$X_i$`，纵轴代表变量
`$Y_i$`，每组数据
`$(X_i, Y_i)$`在坐标系中用一个点表示，
`$n$`组数据在坐标系中形成的
`$n$`个点称为散点，由坐标及其散点形成的二维数据图。

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### （案例）汽车油耗：绘制散点图

**案例说明**：研究人员希望了解汽车油耗的情况，收集了汽车车重、轴距、气缸数量等的数据信息（见下表）：

<div id="htmlwidget-1e3f05716a1411acd9c6" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-1e3f05716a1411acd9c6">{"x":{"filter":"none","data":[["Mazda RX4","Mazda RX4 Wag","Datsun 710","Hornet 4 Drive","Hornet Sportabout","Valiant","Duster 360","Merc 240D","Merc 230","Merc 280","Merc 280C","Merc 450SE","Merc 450SL","Merc 450SLC","Cadillac Fleetwood","Lincoln Continental","Chrysler Imperial","Fiat 128","Honda Civic","Toyota Corolla","Toyota Corona","Dodge Challenger","AMC Javelin","Camaro Z28","Pontiac Firebird","Fiat X1-9","Porsche 914-2","Lotus Europa","Ford Pantera L","Ferrari Dino","Maserati Bora","Volvo 142E"],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32],[21,21,22.8,21.4,18.7,18.1,14.3,24.4,22.8,19.2,17.8,16.4,17.3,15.2,10.4,10.4,14.7,32.4,30.4,33.9,21.5,15.5,15.2,13.3,19.2,27.3,26,30.4,15.8,19.7,15,21.4],[6,6,4,6,8,6,8,4,4,6,6,8,8,8,8,8,8,4,4,4,4,8,8,8,8,4,4,4,8,6,8,4],[160,160,108,258,360,225,360,146.7,140.8,167.6,167.6,275.8,275.8,275.8,472,460,440,78.7,75.7,71.1,120.1,318,304,350,400,79,120.3,95.1,351,145,301,121],[110,110,93,110,175,105,245,62,95,123,123,180,180,180,205,215,230,66,52,65,97,150,150,245,175,66,91,113,264,175,335,109],[3.9,3.9,3.85,3.08,3.15,2.76,3.21,3.69,3.92,3.92,3.92,3.07,3.07,3.07,2.93,3,3.23,4.08,4.93,4.22,3.7,2.76,3.15,3.73,3.08,4.08,4.43,3.77,4.22,3.62,3.54,4.11],[2.62,2.875,2.32,3.215,3.44,3.46,3.57,3.19,3.15,3.44,3.44,4.07,3.73,3.78,5.25,5.424,5.345,2.2,1.615,1.835,2.465,3.52,3.435,3.84,3.845,1.935,2.14,1.513,3.17,2.77,3.57,2.78],[16.46,17.02,18.61,19.44,17.02,20.22,15.84,20,22.9,18.3,18.9,17.4,17.6,18,17.98,17.82,17.42,19.47,18.52,19.9,20.01,16.87,17.3,15.41,17.05,18.9,16.7,16.9,14.5,15.5,14.6,18.6],[0,0,1,1,0,1,0,1,1,1,1,0,0,0,0,0,0,1,1,1,1,0,0,0,0,1,0,1,0,0,0,1],[1,1,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,0,0,0,0,0,1,1,1,1,1,1,1],[4,4,4,3,3,3,3,4,4,4,4,3,3,3,3,3,3,4,4,4,3,3,3,3,3,4,5,5,5,5,5,4],[4,4,1,1,2,1,4,2,2,4,4,3,3,3,4,4,4,1,2,1,1,2,2,4,2,1,2,2,4,6,8,2]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>index<\/th>\n      <th>mpg<\/th>\n      <th>cyl<\/th>\n      <th>disp<\/th>\n      <th>hp<\/th>\n      <th>drat<\/th>\n      <th>wt<\/th>\n      <th>qsec<\/th>\n      <th>vs<\/th>\n      <th>am<\/th>\n      <th>gear<\/th>\n      <th>carb<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":5,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":[],"jsHooks":[]}</script>

]

]

]

---

## 数据未分组：统计制图6（散点图）

**气泡图（bubble chart）**：显示**三个变量**之间的关系，
图中数据点的大小依赖于第三个变量。

---

### （案例）人均寿命：绘制气泡图

**案例说明**：下表给出了各个地区在2007年的人均寿命、人均GDP等数据。

<div id="htmlwidget-e5502f6e1e2581fcba31" style="width:100%;height:auto;" class="datatables html-widget"></div>
<script type="application/json" data-for="htmlwidget-e5502f6e1e2581fcba31">{"x":{"filter":"none","data":[["1","2","3","4","5","6","7","8","9","10","11","12","13","14","15","16","17","18","19","20","21","22","23","24","25","26","27","28","29","30","31","32","33","34","35","36","37","38","39","40","41","42","43","44","45","46","47","48","49","50","51","52","53","54","55","56","57","58","59","60","61","62","63","64","65","66","67","68","69","70","71","72","73","74","75","76","77","78","79","80","81","82","83","84","85","86","87","88","89","90","91","92","93","94","95","96","97","98","99","100","101","102","103","104","105","106","107","108","109","110","111","112","113","114","115","116","117","118","119","120","121","122","123","124","125","126","127","128","129","130","131","132","133","134","135","136","137","138","139","140","141","142"],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99,100,101,102,103,104,105,106,107,108,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141,142],["Afghanistan","Albania","Algeria","Angola","Argentina","Australia","Austria","Bahrain","Bangladesh","Belgium","Benin","Bolivia","Bosnia and Herzegovina","Botswana","Brazil","Bulgaria","Burkina Faso","Burundi","Cambodia","Cameroon","Canada","Central African Republic","Chad","Chile","China","Colombia","Comoros","Congo, Dem. Rep.","Congo, Rep.","Costa Rica","Cote d'Ivoire","Croatia","Cuba","Czech Republic","Denmark","Djibouti","Dominican Republic","Ecuador","Egypt","El Salvador","Equatorial Guinea","Eritrea","Ethiopia","Finland","France","Gabon","Gambia","Germany","Ghana","Greece","Guatemala","Guinea","Guinea-Bissau","Haiti","Honduras","Hong Kong, China","Hungary","Iceland","India","Indonesia","Iran","Iraq","Ireland","Israel","Italy","Jamaica","Japan","Jordan","Kenya","Korea, Dem. Rep.","Korea, Rep.","Kuwait","Lebanon","Lesotho","Liberia","Libya","Madagascar","Malawi","Malaysia","Mali","Mauritania","Mauritius","Mexico","Mongolia","Montenegro","Morocco","Mozambique","Myanmar","Namibia","Nepal","Netherlands","New Zealand","Nicaragua","Niger","Nigeria","Norway","Oman","Pakistan","Panama","Paraguay","Peru","Philippines","Poland","Portugal","Puerto Rico","Reunion","Romania","Rwanda","Sao Tome and Principe","Saudi Arabia","Senegal","Serbia","Sierra Leone","Singapore","Slovak Republic","Slovenia","Somalia","South Africa","Spain","Sri Lanka","Sudan","Swaziland","Sweden","Switzerland","Syria","Taiwan","Tanzania","Thailand","Togo","Trinidad and Tobago","Tunisia","Turkey","Uganda","United Kingdom","United States","Uruguay","Venezuela","Vietnam","West Bank and Gaza","Yemen, Rep.","Zambia","Zimbabwe"],["Asia","Europe","Africa","Africa","Americas","Oceania","Europe","Asia","Asia","Europe","Africa","Americas","Europe","Africa","Americas","Europe","Africa","Africa","Asia","Africa","Americas","Africa","Africa","Americas","Asia","Americas","Africa","Africa","Africa","Americas","Africa","Europe","Americas","Europe","Europe","Africa","Americas","Americas","Africa","Americas","Africa","Africa","Africa","Europe","Europe","Africa","Africa","Europe","Africa","Europe","Americas","Africa","Africa","Americas","Americas","Asia","Europe","Europe","Asia","Asia","Asia","Asia","Europe","Asia","Europe","Americas","Asia","Asia","Africa","Asia","Asia","Asia","Asia","Africa","Africa","Africa","Africa","Africa","Asia","Africa","Africa","Africa","Americas","Asia","Europe","Africa","Africa","Asia","Africa","Asia","Europe","Oceania","Americas","Africa","Africa","Europe","Asia","Asia","Americas","Americas","Americas","Asia","Europe","Europe","Americas","Africa","Europe","Africa","Africa","Asia","Africa","Europe","Africa","Asia","Europe","Europe","Africa","Africa","Europe","Asia","Africa","Africa","Europe","Europe","Asia","Asia","Africa","Asia","Africa","Americas","Africa","Europe","Africa","Europe","Americas","Americas","Americas","Asia","Asia","Asia","Africa","Africa"],[43.828,76.423,72.301,42.731,75.32,81.235,79.829,75.635,64.062,79.441,56.728,65.554,74.852,50.728,72.39,73.005,52.295,49.58,59.723,50.43,80.653,44.741,50.651,78.553,72.961,72.889,65.152,46.462,55.322,78.782,48.328,75.748,78.273,76.486,78.332,54.791,72.235,74.994,71.338,71.878,51.579,58.04,52.947,79.313,80.657,56.735,59.448,79.406,60.022,79.483,70.259,56.007,46.388,60.916,70.198,82.208,73.338,81.757,64.698,70.65,70.964,59.545,78.885,80.745,80.546,72.567,82.603,72.535,54.11,67.297,78.623,77.588,71.993,42.592,45.678,73.952,59.443,48.303,74.241,54.467,64.164,72.801,76.195,66.803,74.543,71.164,42.082,62.069,52.906,63.785,79.762,80.204,72.899,56.867,46.859,80.196,75.64,65.483,75.537,71.752,71.421,71.688,75.563,78.098,78.746,76.442,72.476,46.242,65.528,72.777,63.062,74.002,42.568,79.972,74.663,77.926,48.159,49.339,80.941,72.396,58.556,39.613,80.884,81.701,74.143,78.4,52.517,70.616,58.42,69.819,73.923,71.777,51.542,79.425,78.242,76.384,73.747,74.249,73.422,62.698,42.384,43.487],[31889923,3600523,33333216,12420476,40301927,20434176,8199783,708573,150448339,10392226,8078314,9119152,4552198,1639131,190010647,7322858,14326203,8390505,14131858,17696293,33390141,4369038,10238807,16284741,1318683096,44227550,710960,64606759,3800610,4133884,18013409,4493312,11416987,10228744,5468120,496374,9319622,13755680,80264543,6939688,551201,4906585,76511887,5238460,61083916,1454867,1688359,82400996,22873338,10706290,12572928,9947814,1472041,8502814,7483763,6980412,9956108,301931,1110396331,223547000,69453570,27499638,4109086,6426679,58147733,2780132,127467972,6053193,35610177,23301725,49044790,2505559,3921278,2012649,3193942,6036914,19167654,13327079,24821286,12031795,3270065,1250882,108700891,2874127,684736,33757175,19951656,47761980,2055080,28901790,16570613,4115771,5675356,12894865,135031164,4627926,3204897,169270617,3242173,6667147,28674757,91077287,38518241,10642836,3942491,798094,22276056,8860588,199579,27601038,12267493,10150265,6144562,4553009,5447502,2009245,9118773,43997828,40448191,20378239,42292929,1133066,9031088,7554661,19314747,23174294,38139640,65068149,5701579,1056608,10276158,71158647,29170398,60776238,301139947,3447496,26084662,85262356,4018332,22211743,11746035,12311143],[974.5803384,5937.029526,6223.367465,4797.231267,12779.37964,34435.36744,36126.4927,29796.04834,1391.253792,33692.60508,1441.284873,3822.137084,7446.298803,12569.85177,9065.800825,10680.79282,1217.032994,430.0706916,1713.778686,2042.09524,36319.23501,706.016537,1704.063724,13171.63885,4959.114854,7006.580419,986.1478792,277.5518587,3632.557798,9645.06142,1544.750112,14619.22272,8948.102923,22833.30851,35278.41874,2082.481567,6025.374752,6873.262326,5581.180998,5728.353514,12154.08975,641.3695236,690.8055759,33207.0844,30470.0167,13206.48452,752.7497265,32170.37442,1327.60891,27538.41188,5186.050003,942.6542111,579.231743,1201.637154,3548.330846,39724.97867,18008.94444,36180.78919,2452.210407,3540.651564,11605.71449,4471.061906,40675.99635,25523.2771,28569.7197,7320.880262,31656.06806,4519.461171,1463.249282,1593.06548,23348.13973,47306.98978,10461.05868,1569.331442,414.5073415,12057.49928,1044.770126,759.3499101,12451.6558,1042.581557,1803.151496,10956.99112,11977.57496,3095.772271,9253.896111,3820.17523,823.6856205,944,4811.060429,1091.359778,36797.93332,25185.00911,2749.320965,619.6768924,2013.977305,49357.19017,22316.19287,2605.94758,9809.185636,4172.838464,7408.905561,3190.481016,15389.92468,20509.64777,19328.70901,7670.122558,10808.47561,863.0884639,1598.435089,21654.83194,1712.472136,9786.534714,862.5407561,47143.17964,18678.31435,25768.25759,926.1410683,9269.657808,28821.0637,3970.095407,2602.394995,4513.480643,33859.74835,37506.41907,4184.548089,28718.27684,1107.482182,7458.396327,882.9699438,18008.50924,7092.923025,8458.276384,1056.380121,33203.26128,42951.65309,10611.46299,11415.80569,2441.576404,3025.349798,2280.769906,1271.211593,469.7092981]],"container":"<table class=\"display\">\n  <thead>\n    <tr>\n      <th> <\/th>\n      <th>index<\/th>\n      <th>country<\/th>\n      <th>continent<\/th>\n      <th>lifeExp<\/th>\n      <th>pop<\/th>\n      <th>gdpPercap<\/th>\n    <\/tr>\n  <\/thead>\n<\/table>","options":{"dom":"tip","columnDefs":[{"targets":6,"render":"function(data, type, row, meta) {\n    return type !== 'display' ? data : DTWidget.formatRound(data, 2, 3, \",\", \".\");\n  }"},{"className":"dt-center","targets":"_all"},{"visible":false,"targets":0},{"orderable":false,"targets":0}],"pageLength":5,"order":[],"autoWidth":false,"orderClasses":false,"lengthMenu":[5,10,25,50,100]}},"evals":["options.columnDefs.0.render"],"jsHooks":[]}</script>

]

<img src="03-visualization_files/figure-html/unnamed-chunk-159-1.png" style="display: block; margin: auto;" />
]
]

---

## 数据未分组：统计制图7（雷达图）

**雷达图（radar chart）**：也称为蜘蛛图（spider chart），显示**多个变量**的图示方法。

**用途**：

- 在显示或对比各变量的数值总和时十分有用。

- 假定各变量的取值具有相同的正负号，总的绝对值与图形所围成的区域成正比。

- 可用于研究多个样本之间的相似程度。

---
exclude: true

## （案例）领域发展评估

---

### （案例）领域发展评估：绘制雷达图

**案例说明**：下表给出了三个学生在不同领域发展的评分结果。

<div id="htmlwidget-dde24bae1d8a0a2981a4" style="width:100%;height:auto;" class="datatables html-widget"></div>
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]

]

<img src="03-visualization_files/figure-html/unnamed-chunk-164-1.png" style="display: block; margin: auto;" />
]

]

---

## 数据分布形态：概述

- 正态分布，也称正态曲线

- 偏态分布，或称偏态曲线

]

其他分布形态：

- U型分布

- 双峰分布

- J型分布

- 反J型分布

]

<div class="notes">
<p>待完成：提供示例图形，给出代表分布类型示例。</p>
</div>

---

## 数据分布形态：偏度系数

**偏度（Skewness）系数**：分布形态的一个重要衡量标准就是分布偏度。一组数据分布偏度的计算是复杂的，但使用统计软件可以很容易的计算出偏度系数。偏度系数
`$SK$`的理论计算公式如下：

`$$\begin{align}
SK = \frac{n}{(n-1)(n-2)} \sum_1^n{\left(\frac{X_i-\bar{X}}{S_X}\right)^3}
\end{align}$$`

> 其中：
`$n$`表示样本数；
`$S_X$`表示样本标准差
`$S_X =\sqrt{\frac{\sum_1^n{(X_i- \bar{X})^2}}{n-1}}$`。

---

## 数据分布形态：偏度系数

- 若偏度系数
`$SK = 0$`，则数据分布是对称的（无偏的），此时均值
和中位数相等，也即：
`$\bar{X} = M_e$`。

- 若偏度系数
`$SK < 0$`，则数据分布是非对称的（左偏的），此时均值小于中位数，也即：
`$\bar{X} < M_e$`。

- 若偏度系数
`$SK > 0$`，则数据分布是非对称的（左偏的），此时均值大于中位数，也即：
`$\bar{X} > M_e$`。

---

### （示例）数据分布形态：常见形态

]

]

]

---

### （示例）数据分布形态：其他形态

]

]

]

]

---

## 数据分布形态：峰度系数

**峰度（Kurtosis）系数**：峰度刻画数据分布的拖尾长度和集中度。峰度系数
`$KT$`的理论计算公式如下：

`$$\begin{align}
KT = \frac{n(n+1)}{(n-1)(n-2)(n-3)} \frac{\sum_{i=1}^n{(X_i-\bar{X})^4}}{S_X^4} - \frac{3(n-1)^2}{(n-2)(n-3)}
\end{align}$$`

> 其中：
`$n$`表示样本数；
`$S_X$`表示样本标准差
`$S_X =\sqrt{\frac{\sum_1^n{(X_i- \bar{X})^2}}{n-1}}$`。

- 若峰度系数
`$KT = 0$`，则数据分布是**常峰态的**。

- 若峰度系数
`$KT < 0$`，则数据分布是**低峰态的**。

- 若峰度系数
`$KT > 0$`，则数据分布是**尖峰态的**。

---

### （示例）数据分布形态：不同的峰态形状

---

## 统计制表：结构

统计表的结构与内容一般为：

从**形式**上看：统计表由总标题、横行标题、纵栏标题、指标数值构成。

从**内容**上看：统计表由主词和宾词两部分构成。

- 主词：说明总体或总体的分组。

- 宾词：用哪些指标数值来说明总体或总体的分组。

---

### （示例）统计指标的形式和规范

---

## 统计制表：特点

统计表的特点

- 开口式

- 上下有基线

- 编号：主词一般按A、B、C…，宾词按1、2、3…

- 有计量单位

- 表中不允许有空格：若不需要此资料则用“-”;暂缺某资料则用“……”

---

## 统计制表：设计准则

统计表的一般设计准则包括：

- 合理安排统计表的结构

- 总标题内容应满足3W要求

- 数据计量单位相同时，可放在表的右上角标明，不同时应放在每个变量后或单列出一列标明

- 表中的上下两条横线一般用粗线，其他线用细线

- 通常情况下，统计表的左右两边不封口

- 表中的数据一般是右对齐，有小数点时应以小数点对齐，而且小数点的位数应统一

- 对于没有数字的表格单元，一般用“—”表示

- 必要时可在表的下方加上注释

???

3W是指标题内容需要表明统计数据的时间（When）、地点（Where）以及何种数据（What）

---
layout: false
class: center, middle, duke-softblue ,hide_logo
name: nice

# 3.4 合理使用图表

### 图表体系和要素

### 鉴别图形优劣的准则

---
layout: true

---
exclude: true

## 准备：字体

准备字体库

```
Warning: package 'showtext' was built under R version 4.0.5
```

```
Warning: package 'sysfonts' was built under R version 4.0.5
```

```
[1] "sans"                "serif"               "mono"               
[4] "wqy-microhei"        "source-han-serif-cn"
```

---
exclude: true

## 准备：数据

准备数据

---
exclude: true

## 准备：画图模板

---

### 制图体系：绘图区 panel

]

<img src="03-visualization_files/figure-html/unnamed-chunk-181-1.png" style="display: block; margin: auto;" />
]

]

]

---

### 制图体系：坐标轴1 axis

]

]

]

]

---

### 制图体系：坐标轴2 axis

]

<img src="03-visualization_files/figure-html/unnamed-chunk-189-1.png" style="display: block; margin: auto;" />
]

]

]

---

### 制图体系：坐标轴3 axis

]

]

]

---

### 制图体系：图形类型 geom_xx

]

]

<img src="03-visualization_files/figure-html/unnamed-chunk-197-1.png" style="display: block; margin: auto;" />
]

]

---

### 制图体系：变量数值 data value

---

### 制图体系：图例 legend

]

]

---

### 制图体系：图注 footnote和图题 caption

]

<div class="figure" style="text-align: center">
<img src="03-visualization_files/figure-html/unnamed-chunk-203-1.png" alt="图3-1:plot caption演示"  />
<p class="caption">图3-1:plot caption演示</p>
</div>

]

---

### 制表体系

表格要素包括：表序号（numbering）、表题（title）、表头（header）、主体（body）和表注（footer）等部分构成。

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1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-a9e3e599{width:64.1pt;background-color:transparent;vertical-align: bottom;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-a9e3e59a{width:101.1pt;background-color:transparent;vertical-align: bottom;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-a9e3e59b{width:97.9pt;background-color:transparent;vertical-align: bottom;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}.cl-a9e3e59c{width:106pt;background-color:transparent;vertical-align: bottom;border-bottom: 2pt solid rgba(102, 102, 102, 1.00);border-top: 2pt solid rgba(102, 102, 102, 1.00);border-left: 0 solid rgba(0, 0, 0, 1.00);border-right: 0 solid rgba(0, 0, 0, 1.00);margin-bottom:0;margin-top:0;margin-left:0;margin-right:0;}</style><table class='cl-a9ef317e'><caption class="">表3-2：iris dataset数据集</caption><thead><tr style="overflow-wrap:break-word;"><td class="cl-a9e3e59c"><p class="cl-a9e34954"><span class="cl-a9e32244">Sepal.Length</span><span class="cl-a9e32245">a</span></p></td><td class="cl-a9e3e59b"><p class="cl-a9e34954"><span class="cl-a9e32244">Sepal.Width</span><span class="cl-a9e32245">b</span></p></td><td class="cl-a9e3e59a"><p class="cl-a9e34954"><span class="cl-a9e32244">Petal.Length</span><span class="cl-a9e32245">c</span></p></td><td class="cl-a9e3e598"><p class="cl-a9e34954"><span class="cl-a9e32244">Petal.Width</span></p></td><td class="cl-a9e3e599"><p class="cl-a9e34954"><span class="cl-a9e32244">Species</span></p></td></tr></thead><tbody><tr style="overflow-wrap:break-word;"><td class="cl-a9e3be7d"><p class="cl-a9e34955"><span class="cl-a9e32244">5.1</span></p></td><td class="cl-a9e3be7e"><p class="cl-a9e34955"><span class="cl-a9e32244">3.5</span></p></td><td class="cl-a9e3be7a"><p class="cl-a9e34955"><span class="cl-a9e32244">1.4</span></p></td><td class="cl-a9e3be7b"><p class="cl-a9e34955"><span class="cl-a9e32244">0.2</span></p></td><td class="cl-a9e3be7c"><p class="cl-a9e34955"><span class="cl-a9e32244">setosa</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-a9e3be7d"><p class="cl-a9e34955"><span class="cl-a9e32244">4.9</span></p></td><td class="cl-a9e3be7e"><p class="cl-a9e34955"><span class="cl-a9e32244">3.0</span></p></td><td class="cl-a9e3be7a"><p class="cl-a9e34955"><span class="cl-a9e32244">1.4</span></p></td><td class="cl-a9e3be7b"><p class="cl-a9e34955"><span class="cl-a9e32244">0.2</span></p></td><td class="cl-a9e3be7c"><p class="cl-a9e34955"><span class="cl-a9e32244">setosa</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-a9e3be7d"><p class="cl-a9e34955"><span class="cl-a9e32244">4.7</span></p></td><td class="cl-a9e3be7e"><p class="cl-a9e34955"><span class="cl-a9e32244">3.2</span></p></td><td class="cl-a9e3be7a"><p class="cl-a9e34955"><span class="cl-a9e32244">1.3</span></p></td><td class="cl-a9e3be7b"><p class="cl-a9e34955"><span class="cl-a9e32244">0.2</span></p></td><td class="cl-a9e3be7c"><p class="cl-a9e34955"><span class="cl-a9e32244">setosa</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-a9e3be7d"><p class="cl-a9e34955"><span class="cl-a9e32244">4.6</span></p></td><td class="cl-a9e3be7e"><p class="cl-a9e34955"><span class="cl-a9e32244">3.1</span></p></td><td class="cl-a9e3be7a"><p class="cl-a9e34955"><span class="cl-a9e32244">1.5</span></p></td><td class="cl-a9e3be7b"><p class="cl-a9e34955"><span class="cl-a9e32244">0.2</span></p></td><td class="cl-a9e3be7c"><p class="cl-a9e34955"><span class="cl-a9e32244">setosa</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-a9e3be7d"><p class="cl-a9e34955"><span class="cl-a9e32244">5.0</span></p></td><td class="cl-a9e3be7e"><p class="cl-a9e34955"><span class="cl-a9e32244">3.6</span></p></td><td class="cl-a9e3be7a"><p class="cl-a9e34955"><span class="cl-a9e32244">1.4</span></p></td><td class="cl-a9e3be7b"><p class="cl-a9e34955"><span class="cl-a9e32244">0.2</span></p></td><td class="cl-a9e3be7c"><p class="cl-a9e34955"><span class="cl-a9e32244">setosa</span></p></td></tr><tr style="overflow-wrap:break-word;"><td class="cl-a9e3be81"><p class="cl-a9e34955"><span class="cl-a9e32244">5.4</span></p></td><td class="cl-a9e3be7f"><p class="cl-a9e34955"><span class="cl-a9e32244">3.9</span></p></td><td class="cl-a9e3be80"><p 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---

## 良好图表应具备的基本特征

- 服务于一个明确的目的

- 显示数据

- 强调数据之间的比较

- 有对图表的统计描述和文字说明

- 让读者把注意力集中在图表的内容上，而不是制作图表的程序上

- 避免歪曲

---

## 鉴别图表优劣的准则

- 表述数据的真实情况

- 使复杂的观点得到简明、确切、高效的阐述

- 精心设计、有助于洞察问题的实质

- 能在最短的时间内以最少的笔墨给读者提供最大量的信息

- 多维度地对问题进行客观反映

---

## 制图常见误区：非零起始点1

---

## 制图常见误区：非零起始点2

---

## 制图常见误区：图片比例拉伸失调

---

## 制图常见误区：炫技乱人心

---

## 制图常见误区：视觉误导1

---

## 制图常见误区：视觉误导2

---

## 制图常见误区：目标不明确

---

## 图设计要点：饼图VS条形图？

**点评**：一般来讲表述市场份额是100%，所以大家习惯用饼图表述，研究表明人们更习惯从条形图来比较大小，更醒目的看到差异！

---

## 图设计要点：线形图VS柱状图？

**点评**：X轴是时间，是时间序列数据，所以折线图更能够感知的趋势、模式的变化！当然如果你表现的是不同品牌的市场份额，柱状图也是可以的！

---

## 图设计要点：平面图VS立体图？

**点评**：二维图更适合人们观察，三维并不适合观察，毕竟人类视觉空间最低维度是二维！另时序数据应该采用折线图表述趋势！

---

## 图设计要点：3D VS 2D？

**点评**：尽量不用用三维图，但是大家是不是会把信息按某个维度作出分散的二维图呢？一定注意要用统一的纵坐标，否则是四张图，要贴成一张图！

---

## 图设计要点：颜色VS数据？

**点评**：如果选上面的打印都费墨，坚持简单是最好的。当然如果有艺术细胞的话，背景也是可以更为生动些，但是更多是考虑展示结果！

---

## 图设计要点：选色VS选图？

**点评**：比较是展示数据差异的好法子，但是如果读者不容易看出差别的话，那么比较就毫无意义。确保选择最合适的比较方法。

---

## 图设计要点：饼图-排序VS分块？

**点评**：理论上，一个饼图不应该分割超过5块。注意排序，最大一块12点钟开始,顺时针方向旋转。剩余部分再降序排列，顺时针。

---

## 图设计要点：线图-实线VS虚线？

**点评**：虚线容易分散注意力。相反,使用实线和颜色,反而容易区分彼此的区别。

---

## 图设计要点：条形图-排序数据VS名称？

**点评**：你的内容应该以一种合乎逻辑的和直观的方式来引导读者了解数据。所以，记得将数据类别按字母顺序、大小顺序、或数据值进行排序。

---

## 图设计要点：柱状图-宽度VS间距？

**点评**：或许你的报告很有创意，非常精彩，但是记得图表设计水平也要跟上。条形图之间的间隔应该是1/2栏宽度。

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## 图设计要点：面积图-堆叠VS透明度？

**点评**：确保没有数据丢失或被设计修改。例如，使用标准的面积图时，可以添加透明度，确保读者可以看到所有数据。

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## 图设计要点：散点图-原始VS趋势？

**点评**：应该使图表尽可能轻松地帮助读者理解数据。例如，在散点图中添加趋势线来强调的趋势。

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## 图设计要点：气泡图-形状VS数值？

**点评**：确保所有可视化方式是准确的。例如，气泡图大小应该根据区域扩展，而不是直径。

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## 图设计要点：热力图-颜色堆VS颜色系？

**点评**：颜色用得太花，会给数据增加不可承受之重，相反，应该采用同一色系，或者类比色。

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## 表设计要点：交叉表-封闭VS开放？

**点评**：下表更加清晰明快！我们习惯采用中国式上表，一般都是封闭边框线的。但是我们如果经常看英文的论文，你会发现很多论文都是下面开放式三线表！

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## 表设计要点：交叉表-颜色VS线条？

**点评**：应选择上表。网格线会让我们看不清晰。当然颜色也是非常重要的，要学会使用条件格式规则调色，还有如字体、数值、对齐等格式问题！

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