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中心极限定理：偏态总体样本均值的分布

中心极限定理：偏态总体样本均值的分布
几何画板及绘图内容加载中，请稍等……
2018-07-15 08:38
函数概率统计滑块动画函数图像
① 本范例通过动态模拟，直观展示从偏态总体中抽取样本后，样本均值随样本量增大逐渐趋近正态分布的现象。② 核心数学概念是中心极限定理（CLT），涉及总体分布、样本均值、标准差、直方图以及正态逼近。③ 作图要点：使用GeoGebra的Sample命令从偏态总体中抽取样本，计算样本均值（Mean）和标准差（SD），并用Histogram命令绘制样本均值的分布直方图；同时利用LaTeX标注公式和说明，对象编号如A350等用于存储中间数据。④ 适合高中至大学阶段的统计学教学，尤其用于理解抽样分布和中心极限定理的直观演示，也可用于探究样本量对分布形状的影响。

GeoGebra 命令及参数

  1. Sample(list1, SampleSize) → F51
  2. Mean(F51) → G51
  3. Sample(list1, SampleSize) → F50
  4. Mean(F50) → G50
  5. Sample(list1, SampleSize) → F49
  6. Mean(F49) → G49
  7. Sample(list1, SampleSize) → F48
  8. Mean(F48) → G48
  9. Sample(list1, SampleSize) → F47
  10. Mean(F47) → G47
  11. Sample(list1, SampleSize) → F46
  12. Mean(F46) → G46
  13. Sample(list1, SampleSize) → F45
  14. Mean(F45) → G45
  15. Sample(list1, SampleSize) → F44
  16. Mean(F44) → G44
  17. Sample(list1, SampleSize) → F43
  18. Mean(F43) → G43
  19. Sample(list1, SampleSize) → F42
  20. Mean(F42) → G42
  21. Sample(list1, SampleSize) → F41
  22. Mean(F41) → G41
  23. Sample(list1, SampleSize) → F40
  24. Mean(F40) → G40
  25. Sample(list1, SampleSize) → F39
  26. Mean(F39) → G39
  27. Sample(list1, SampleSize) → F38
  28. Mean(F38) → G38
  29. Sample(list1, SampleSize) → F37
  30. Mean(F37) → G37
  31. Sample(list1, SampleSize) → F36
  32. Mean(F36) → G36
  33. Sample(list1, SampleSize) → F35
  34. Mean(F35) → G35
  35. Sample(list1, SampleSize) → F34
  36. Mean(F34) → G34
  37. Sample(list1, SampleSize) → F33
  38. Mean(F33) → G33
  39. Sample(list1, SampleSize) → F32
  40. Mean(F32) → G32
  41. Sample(list1, SampleSize) → F31
  42. Mean(F31) → G31
  43. Sample(list1, SampleSize) → F30
  44. Mean(F30) → G30
  45. Sample(list1, SampleSize) → F29
  46. Mean(F29) → G29
  47. Sample(list1, SampleSize) → F28
  48. Mean(F28) → G28
  49. Sample(list1, SampleSize) → F27
  50. Mean(F27) → G27
  51. Sample(list1, SampleSize) → F26
  52. Mean(F26) → G26
  53. Sample(list1, SampleSize) → F25
  54. Mean(F25) → G25
  55. Sample(list1, SampleSize) → F24
  56. Mean(F24) → G24
  57. Sample(list1, SampleSize) → F23
  58. Mean(F23) → G23
  59. Sample(list1, SampleSize) → F22
  60. Mean(F22) → G22
  61. Sample(list1, SampleSize) → F21
  62. Mean(F21) → G21
  63. Sample(list1, SampleSize) → F20
  64. Mean(F20) → G20
  65. Sample(list1, SampleSize) → F19
  66. Mean(F19) → G19
  67. Sample(list1, SampleSize) → F18
  68. Mean(F18) → G18
  69. Sample(list1, SampleSize) → F17
  70. Mean(F17) → G17
  71. Sample(list1, SampleSize) → F16
  72. Mean(F16) → G16
  73. Sample(list1, SampleSize) → F15
  74. Mean(F15) → G15
  75. Sample(list1, SampleSize) → F14
  76. Mean(F14) → G14
  77. Sample(list1, SampleSize) → F13
  78. Mean(F13) → G13
  79. Sample(list1, SampleSize) → F12
  80. Mean(F12) → G12
  81. Sample(list1, SampleSize) → F11
  82. Mean(F11) → G11
  83. Sample(list1, SampleSize) → F10
  84. Mean(F10) → G10
  85. Sample(list1, SampleSize) → F9
  86. Mean(F9) → G9
  87. Sample(list1, SampleSize) → F8
  88. Mean(F8) → G8
  89. Sample(list1, SampleSize) → F7
  90. Mean(F7) → G7
  91. Sample(list1, SampleSize) → F6
  92. Mean(F6) → G6
  93. Sample(list1, SampleSize) → F5
  94. Mean(F5) → G5
  95. Sample(list1, SampleSize) → F4
  96. Mean(F4) → G4
  97. Sample(list1, SampleSize) → F3
  98. Mean(F3) → G3
  99. Sample(list1, SampleSize) → F2
  100. Mean(F2) → G2
  101. Sample(list1, SampleSize) → F1
  102. Mean(F1) → G1
  103. Mean(list5) → H2
  104. SD(list5) → H3
  105. LaTeX(MeanOfSampleMeans, true, true) → text5
  106. LaTeX(SDOfSampleMeans, true, true) → text6
  107. Histogram(list4, list5, true, 2) → h
  108. Mean(list1) → MeanOfPopulation
  109. SD(list1) → D2
  110. Histogram(list2, list1, false, 2) → a
  111. LaTeX(MeanOfPopulation, true, true) → text1
  112. SD(list1) → SDOfPopulation
  113. LaTeX(SDOfPopulation, true, true) → text2

AI 绘图提示语参考

绘制一个示例，展示当样本大小增加时，样本均值的分布如何趋向于正态分布，即使总体是偏斜的。首先从一个偏斜的总体中抽取多个样本，计算每个样本的均值，然后绘制这些均值的直方图，观察其形状的变化。
以上提示语为根据原始绘图命令整理而来，仅供参考。