題目：模擬產生統計專業同學的名單（學號區分），記錄數學分析、線性代數、概率統計三科成績，然後進行一些統計分析

  1. > num=seq(10378001,10378100)
  2. > num
  3.   [1] 10378001 10378002 10378003 10378004 10378005 10378006 10378007 10378008
  4.   [9] 10378009 10378010 10378011 10378012 10378013 10378014 10378015 10378016
  5.  [17] 10378017 10378018 10378019 10378020 10378021 10378022 10378023 10378024
  6.  [25] 10378025 10378026 10378027 10378028 10378029 10378030 10378031 10378032
  7.  [33] 10378033 10378034 10378035 10378036 10378037 10378038 10378039 10378040
  8.  [41] 10378041 10378042 10378043 10378044 10378045 10378046 10378047 10378048
  9.  [49] 10378049 10378050 10378051 10378052 10378053 10378054 10378055 10378056
  10.  [57] 10378057 10378058 10378059 10378060 10378061 10378062 10378063 10378064
  11.  [65] 10378065 10378066 10378067 10378068 10378069 10378070 10378071 10378072
  12.  [73] 10378073 10378074 10378075 10378076 10378077 10378078 10378079 10378080
  13.  [81] 10378081 10378082 10378083 10378084 10378085 10378086 10378087 10378088
  14.  [89] 10378089 10378090 10378091 10378092 10378093 10378094 10378095 10378096
  15.  [97] 10378097 10378098 10378099 10378100

用runif（產生均勻分佈的隨機數）和rnorm（產生正態分佈的隨機數）

  1. > x1=round(runif(100,min=80,max=100))
  2. > x1
  3.   [1]  81  94  98  86  86  95  88  90  93  86  87  93  93  85  85  87  84  93
  4.  [19]  99  85  99  80  88  93  82  86  89  83  96  99  89  92  87  87  83  86
  5.  [37]  89  88  85  92  86  84  87  86  88  94  89  93  95  99  99  92  89 100
  6.  [55]  92  98  82  88  83  83  94  91  84  81  88  92  98  83  94  95  99  95
  7.  [73]  81  82  86  94  85  83  81  87  98  90  81  81  90  85  80  92  98  82
  8.  [91]  96  96  91  95  80  88  84  87  93  96
  9. > x2=round(rnorm(100,mean=80,sd=7))
  10. > x2
  11.   [1] 72 67 83 81 82 81 73 73 74 84 72 86 87 79 85 70 76 93 73 85 89 77 75 72 82
  12.  [26] 83 85 82 79 88 86 87 83 72 76 90 85 77 81 77 94 74 61 76 92 77 77 74 87 94
  13.  [51] 87 81 66 76 73 75 81 84 89 70 73 86 81 80 79 81 82 74 75 65 77 75 75 87 90
  14.  [76] 74 84 71 85 89 79 80 79 77 90 77 83 80 78 94 85 81 83 82 87 84 86 89 83 75
  15. > x3=round(rnorm(100,mean=83,sd=18))
  16. > x3
  17.   [1]  85 107  96  83  82  60  68 106  52  78 114  78  74  80  76 121  84  90
  18.  [19]  66 105 104 110  94  68  80  84  84 103  99  98 101  82  91  71  96  74
  19.  [37]  82 115  77  70  84  82  74  88  83 100  92  70  77  98 103  58  79  85
  20.  [55]  45  63 101  66  60  70  77  67  83  90  79 100 105  76 103  95  82  78
  21.  [73]  72  54  64  83  85  92  93 120 100  98  82  73  93 110  90 102  81  98
  22.  [91]  91  53 103  74  59  91 110  71  76  92
  23. > x3[which(x3>100)]=100 #將大於100分的成績換成100分
  24. > x3
  25.   [1]  85 100  96  83  82  60  68 100  52  78 100  78  74  80  76 100  84  90
  26.  [19]  66 100 100 100  94  68  80  84  84 100  99  98 100  82  91  71  96  74
  27.  [37]  82 100  77  70  84  82  74  88  83 100  92  70  77  98 100  58  79  85
  28.  [55]  45  63 100  66  60  70  77  67  83  90  79 100 100  76 100  95  82  78
  29.  [73]  72  54  64  83  85  92  93 100 100  98  82  73  93 100  90 100  81  98
  30.  [91]  91  53 100  74  59  91 100  71  76  92

合成數據框並儲存到硬碟

  1. > x=data.frame(num,x1,x2,x3)
  2. > x
  3.          num  x1 x2  x3
  4. 1   10378001  81 72  85
  5. 2   10378002  94 67 100
  6. 3   10378003  98 83  96
  7. 4   10378004  86 81  83
  8. 5   10378005  86 82  82
  9. 6   10378006  95 81  60
  10. 7   10378007  88 73  68
  11. 8   10378008  90 73 100
  12. 9   10378009  93 74  52
  13. 10  10378010  86 84  78
  14. 11  10378011  87 72 100
  15. 12  10378012  93 86  78
  16. 13  10378013  93 87  74
  17. 14  10378014  85 79  80
  18. 15  10378015  85 85  76
  19. 16  10378016  87 70 100
  20. 17  10378017  84 76  84
  21. 18  10378018  93 93  90
  22. 19  10378019  99 73  66
  23. 20  10378020  85 85 100
  24. 21  10378021  99 89 100
  25. 22  10378022  80 77 100
  26. 23  10378023  88 75  94
  27. 24  10378024  93 72  68
  28. 25  10378025  82 82  80
  29. 26  10378026  86 83  84
  30. 27  10378027  89 85  84
  31. 28  10378028  83 82 100
  32. 29  10378029  96 79  99
  33. 30  10378030  99 88  98
  34. 31  10378031  89 86 100
  35. 32  10378032  92 87  82
  36. 33  10378033  87 83  91
  37. 34  10378034  87 72  71
  38. 35  10378035  83 76  96
  39. 36  10378036  86 90  74
  40. 37  10378037  89 85  82
  41. 38  10378038  88 77 100
  42. 39  10378039  85 81  77
  43. 40  10378040  92 77  70
  44. 41  10378041  86 94  84
  45. 42  10378042  84 74  82
  46. 43  10378043  87 61  74
  47. 44  10378044  86 76  88
  48. 45  10378045  88 92  83
  49. 46  10378046  94 77 100
  50. 47  10378047  89 77  92
  51. 48  10378048  93 74  70
  52. 49  10378049  95 87  77
  53. 50  10378050  99 94  98
  54. 51  10378051  99 87 100
  55. 52  10378052  92 81  58
  56. 53  10378053  89 66  79
  57. 54  10378054 100 76  85
  58. 55  10378055  92 73  45
  59. 56  10378056  98 75  63
  60. 57  10378057  82 81 100
  61. 58  10378058  88 84  66
  62. 59  10378059  83 89  60
  63. 60  10378060  83 70  70
  64. 61  10378061  94 73  77
  65. 62  10378062  91 86  67
  66. 63  10378063  84 81  83
  67. 64  10378064  81 80  90
  68. 65  10378065  88 79  79
  69. 66  10378066  92 81 100
  70. 67  10378067  98 82 100
  71. 68  10378068  83 74  76
  72. 69  10378069  94 75 100
  73. 70  10378070  95 65  95
  74. 71  10378071  99 77  82
  75. 72  10378072  95 75  78
  76. 73  10378073  81 75  72
  77. 74  10378074  82 87  54
  78. 75  10378075  86 90  64
  79. 76  10378076  94 74  83
  80. 77  10378077  85 84  85
  81. 78  10378078  83 71  92
  82. 79  10378079  81 85  93
  83. 80  10378080  87 89 100
  84. 81  10378081  98 79 100
  85. 82  10378082  90 80  98
  86. 83  10378083  81 79  82
  87. 84  10378084  81 77  73
  88. 85  10378085  90 90  93
  89. 86  10378086  85 77 100
  90. 87  10378087  80 83  90
  91. 88  10378088  92 80 100
  92. 89  10378089  98 78  81
  93. 90  10378090  82 94  98
  94. 91  10378091  96 85  91
  95. 92  10378092  96 81  53
  96. 93  10378093  91 83 100
  97. 94  10378094  95 82  74
  98. 95  10378095  80 87  59
  99. 96  10378096  88 84  91
  100. 97  10378097  84 86 100
  101. 98  10378098  87 89  71
  102. 99  10378099  93 83  76
  103. 100 10378100  96 75  92
  104. > write.table(x,file="mark.txt",col.names=F,row.name=F,sep=" ")

計算各科平均分

  1. > mean(x)
  2. [1] NA
  3. Warning message:
  4. In mean.default(x) : 引數不是數值也不是邏輯值：回覆NA
  5. > colMeans(x)
  6.         num          x1          x2          x3
  7. 10378050.50       89.24       80.25       83.68
  8. > colMeans(x)[c("x1","x2","x3")]
  9.    x1    x2    x3
  10. 89.24 80.25 83.68
  11. > apply(x,2,mean)
  12.         num          x1          x2          x3
  13. 10378050.50       89.24       80.25       83.68

求各科最高最低分

  1. > apply(x,2,max)
  2.      num       x1       x2       x3
  3. 10378100      100       94      100
  4. > apply(x,2,min)
  5.      num       x1       x2       x3
  6. 10378001       80       61       45

求每人的總分

  1. > apply(x[c("x1","x2","x3")],1,sum)
  2.   [1] 238 261 277 250 250 236 229 263 219 248 259 257 254 244 246 257 244 276
  3.  [19] 238 270 288 257 257 233 244 253 258 265 274 285 275 261 261 230 255 250
  4.  [37] 256 265 243 239 264 240 222 250 263 271 258 237 259 291 286 231 234 261
  5.  [55] 210 236 263 238 232 223 244 244 248 251 246 273 280 233 269 255 258 248
  6.  [73] 228 223 240 251 254 246 259 276 277 268 242 231 273 262 253 272 257 274
  7.  [91] 272 230 274 251 226 263 270 247 252 263

求總分最高的同學

  1. > which.max(apply(x[c("x1","x2","x3")],1,sum))
  2. [1] 50
  3. > x$num[which.max(apply(x[c("x1","x2","x3")],1,sum))]
  4. [1] 10378050

對x1進行直方圖分析

  1. > hist(x$x1)

探索各科成績的關聯關係

  1. > plot(x1,x2)
  2. > plot(x$x1,x$x2)

列聯表分析

  1. > table(x$x1)
  2.  
  3.  80  81  82  83  84  85  86  87  88  89  90  91  92  93  94  95  96  98  99 100
  4.   3   6   4   6   4   6   8   7   7   5   3   2   6   7   5   5   4   5   6   1
  5. > barplot(table(x$x1))

餅圖

  1. > pie(table(x$x1))

箱線圖

  1. > boxplot(x$x1,x$x2,x$x3)

  1. > boxplot(x[2:4],col=c("red","green","blue"),notch=T)#顏色設定

  1. > boxplot(x$x1,x$x2,x$x3,horizontal=T)#水平放置

星相圖

  1. > stars(x[c("x1","x2","x3")])

  1. > stars(x[c("x1","x2","x3")],full=T,draw.segment=T)#雷達圖

  1. > stars(x[c("x1","x2","x3")],full=F,draw.segment=T)#雷達圖（半圓）

臉譜圖

  1. > library(aplpack)
  2. 載入需要的程輯包：tcltk
  3. > faces(x[c("x1","x2","x3")])
  4. effect of variables:
  5.  modified item       Var
  6.  "height of face   " "x1"
  7.  "width of face    " "x2"
  8.  "structure of face" "x3"
  9.  "height of mouth  " "x1"
  10.  "width of mouth   " "x2"
  11.  "smiling          " "x3"
  12.  "height of eyes   " "x1"
  13.  "width of eyes    " "x2"
  14.  "height of hair   " "x3"
  15.  "width of hair   "  "x1"
  16.  "style of hair   "  "x2"
  17.  "height of nose  "  "x3"
  18.  "width of nose   "  "x1"
  19.  "width of ear    "  "x2"
  20.  "height of ear   "  "x3"

其它臉譜圖

  1. > library(TeachingDemos)
  2.  
  3. 載入程輯包：‘TeachingDemos’
  4.  
  5. The following objects are masked from ‘package:aplpack’:
  6.  
  7.     faces, slider
  8.  
  9. > faces2(x)

莖葉圖

  1. > stem(x$x1)
  2.  
  3.   The decimal point is at the |
  4.  
  5.    80 | 000000000
  6.    82 | 0000000000
  7.    84 | 0000000000
  8.    86 | 000000000000000
  9.    88 | 000000000000
  10.    90 | 00000
  11.    92 | 0000000000000
  12.    94 | 0000000000
  13.    96 | 0000
  14.    98 | 00000000000
  15.   100 | 0

QQ圖

可用於判斷是否正態分佈

直線的斜率是標準差，截距是均值

點的分佈越是接近直線，則越接近正態分佈

  1. > qqnorm(x1)
  2. > qqline(x1)
  3. > qqnorm(x3)
  4. > qqline(x3)

散點圖的進一步設定

  1. plot(x$x1,x$x2
  2. main="數學分析與線性代數成績的關係",
  3. xlab="數學分析",
  4. ylab="線性代數",
  5. xlim=c(0,100),
  6. ylim=c(0,100),
  7. xaxs="i",#Set x axis style as internal
  8. yaxs="i",#Set y axis style as internal
  9. col="red",#Set the color of plotting symbol to red
  10. pch=19)#Set the ploting symbol to filled dots