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两个分布的方差比较可视化

两个分布的方差比较可视化
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2020-05-31 06:57
函数概率统计函数图像
该范例通过GeoGebra动态展示两个不同分布的方差对比，直观呈现数据离散程度的差异。核心数学概念包括统计中的均值、方差、标准差以及分布形状。作图要点：使用Segment和Point构造数据点，mean计算均值，stdevp计算总体标准差，BarChart绘制柱状图，Vector表示偏差向量，并利用多个文本对象（text1至text7）标注关键数值。适合高中及大学统计学入门教学，帮助学生理解方差作为离散程度度量的意义，以及不同分布形态对方差的影响。

GeoGebra 命令及参数

  1. Segment((1, 0), (11, 0)) → thexaxis
  2. Point(thexaxis) → A12
  3. Point(thexaxis) → A13
  4. Point(thexaxis) → A14
  5. Point(thexaxis) → A15
  6. Point(thexaxis) → A16
  7. Point(thexaxis) → A17
  8. Point(thexaxis) → A18
  9. Point(thexaxis) → A19
  10. Point(thexaxis) → A20
  11. Point(thexaxis) → A21
  12. Point(thexaxis) → A22
  13. Point(thexaxis) → A23
  14. Point(thexaxis) → A24
  15. Point(thexaxis) → A25
  16. Point(thexaxis) → A26
  17. Point(thexaxis) → A27
  18. Point(thexaxis) → A28
  19. Point(thexaxis) → A29
  20. Point(thexaxis) → A30
  21. Point(thexaxis) → A31
  22. Point(thexaxis) → A32
  23. Point(thexaxis) → A33
  24. Point(thexaxis) → A34
  25. Point(thexaxis) → A35
  26. Point(thexaxis) → A36
  27. Point(thexaxis) → A37
  28. Point(thexaxis) → A38
  29. Point(thexaxis) → A39
  30. Point(thexaxis) → A40
  31. Point(thexaxis) → A41
  32. Point(thexaxis) → A42
  33. Point(thexaxis) → A43
  34. Point(thexaxis) → A44
  35. Point(thexaxis) → A45
  36. Point(thexaxis) → A46
  37. Point(thexaxis) → A47
  38. Point(thexaxis) → A48
  39. Point(thexaxis) → A49
  40. Point(thexaxis) → A50
  41. Point(thexaxis) → B13
  42. Point(thexaxis) → B14
  43. Point(thexaxis) → B15
  44. Point(thexaxis) → B16
  45. Point(thexaxis) → B17
  46. Point(thexaxis) → B18
  47. Point(thexaxis) → B19
  48. Point(thexaxis) → B20
  49. Point(thexaxis) → B21
  50. Point(thexaxis) → B22
  51. Point(thexaxis) → B23
  52. Point(thexaxis) → B24
  53. Point(thexaxis) → B25
  54. Point(thexaxis) → B26
  55. Point(thexaxis) → B27
  56. Point(thexaxis) → B28
  57. Point(thexaxis) → B29
  58. Point(thexaxis) → B30
  59. Point(thexaxis) → B31
  60. Point(thexaxis) → B32
  61. Point(thexaxis) → B33
  62. Point(thexaxis) → B34
  63. Point(thexaxis) → B35
  64. Point(thexaxis) → B36
  65. Point(thexaxis) → B37
  66. Point(thexaxis) → B38
  67. Point(thexaxis) → B39
  68. Point(thexaxis) → B40
  69. Point(thexaxis) → B41
  70. Point(thexaxis) → B42
  71. Point(thexaxis) → B43
  72. Point(thexaxis) → B44
  73. Point(thexaxis) → B45
  74. Point(thexaxis) → B46
  75. Point(thexaxis) → B47
  76. Point(thexaxis) → B48
  77. Point(thexaxis) → B49
  78. Point(thexaxis) → B50
  79. mean(thexs1) → mean1
  80. mean(thexs2) → mean2
  81. Segment((mean1, (meandepth * ymin)), (mean1, 0)) → meanpos1
  82. Segment((mean2, (meandepth * ymin)), (mean2, 0)) → meanpos2
  83. Point(thexaxis) → B12
  84. BarChart(Sequence[11], freq1, 0.8) → dist1
  85. BarChart(Sequence[11], freq2, 0.8) → dist2
  86. Point(thexaxis) → A11
  87. Point(thexaxis) → B11
  88. Point(thexaxis) → A1
  89. Point(thexaxis) → A2
  90. Point(thexaxis) → A3
  91. Point(thexaxis) → A4
  92. Point(thexaxis) → A5
  93. Point(thexaxis) → A6
  94. Point(thexaxis) → A7
  95. Point(thexaxis) → A8
  96. Point(thexaxis) → A9
  97. Point(thexaxis) → A10
  98. Point(thexaxis) → B1
  99. Point(thexaxis) → B2
  100. Point(thexaxis) → B3
  101. Point(thexaxis) → B4
  102. Point(thexaxis) → B5
  103. Point(thexaxis) → B6
  104. Point(thexaxis) → B7
  105. Point(thexaxis) → B8
  106. Point(thexaxis) → B9
  107. Point(thexaxis) → B10
  108. stdevp(thexs1) → sd1
  109. stdevp(thexs2) → sd2
  110. Vector((mean1, (sddepth * ymin)), (mean1 - sd1, (sddepth * ymin))) → sdleft1
  111. Vector((mean1, (sddepth * ymin)), (mean1 + sd1, (sddepth * ymin))) → sdright1
  112. Vector((mean2, (sddepth * ymin)), (mean2 - sd2, (sddepth * ymin))) → sdleft2
  113. Vector((mean2, (sddepth * ymin)), (mean2 + sd2, (sddepth * ymin))) → sdright2

AI 绘图提示语参考

在横轴上绘制50个点，然后在这50个点的基础上分别生成两组数据点，每组25个点，用条形图表示这两组数据的分布情况，并计算每组数据的平均值、标准差和方差，用箭头表示每个数据点到平均值的偏差，最后用文本标注出每组数据的平均值、标准差和方差。
以上提示语为根据原始绘图命令整理而来，仅供参考。