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直方图与正态分布模型

直方图与正态分布模型
几何画板及绘图内容加载中，请稍等……
2015-07-29 21:52
数列概率统计滑块动画函数图像
本范例演示如何利用GeoGebra构建直方图正态分布模型。①图形/现象：生成符合正态分布的随机数序列，并绘制对应的直方图进行可视化展示。②核心数学概念：正态分布（高斯分布）、直方图、随机抽样、概率密度。③作图要点：使用Sequence命令生成随机数序列，RandomNormal命令产生正态分布随机数，CountIf进行条件计数，Histogram命令绘制直方图，DotPlot绘制点图，LaTeX显示数学公式。④适合高中至大学本科概率统计课程，可用于讲解中心极限定理、概率分布拟合等概念。

GeoGebra 命令及参数

  1. Sequence(RandomNormal[0, 1], n, 1, 1000) → list4
  2. RandomNormal(0, 1) → A1
  3. RandomNormal(0, 1) → A2
  4. RandomNormal(0, 1) → A3
  5. RandomNormal(0, 1) → A4
  6. RandomNormal(0, 1) → A5
  7. RandomNormal(0, 1) → A6
  8. RandomNormal(0, 1) → A7
  9. RandomNormal(0, 1) → A8
  10. RandomNormal(0, 1) → A9
  11. RandomNormal(0, 1) → A10
  12. RandomNormal(0, 1) → A11
  13. RandomNormal(0, 1) → A12
  14. RandomNormal(0, 1) → A13
  15. RandomNormal(0, 1) → A14
  16. RandomNormal(0, 1) → A15
  17. RandomNormal(0, 1) → A16
  18. RandomNormal(0, 1) → A17
  19. RandomNormal(0, 1) → A18
  20. RandomNormal(0, 1) → A19
  21. RandomNormal(0, 1) → A20
  22. RandomNormal(0, 1) → A21
  23. RandomNormal(0, 1) → A22
  24. RandomNormal(0, 1) → A23
  25. RandomNormal(0, 1) → A24
  26. RandomNormal(0, 1) → A25
  27. RandomNormal(0, 1) → A26
  28. RandomNormal(0, 1) → A27
  29. RandomNormal(0, 1) → A28
  30. RandomNormal(0, 1) → A29
  31. RandomNormal(0, 1) → A30
  32. RandomNormal(0, 1) → A31
  33. RandomNormal(0, 1) → A32
  34. RandomNormal(0, 1) → A33
  35. RandomNormal(0, 1) → A34
  36. RandomNormal(0, 1) → A35
  37. RandomNormal(0, 1) → A36
  38. RandomNormal(0, 1) → A37
  39. RandomNormal(0, 1) → A38
  40. RandomNormal(0, 1) → A39
  41. RandomNormal(0, 1) → A40
  42. RandomNormal(0, 1) → A41
  43. RandomNormal(0, 1) → A42
  44. RandomNormal(0, 1) → A43
  45. RandomNormal(0, 1) → A44
  46. RandomNormal(0, 1) → A45
  47. RandomNormal(0, 1) → A46
  48. RandomNormal(0, 1) → A47
  49. RandomNormal(0, 1) → A48
  50. RandomNormal(0, 1) → A49
  51. RandomNormal(0, 1) → A50
  52. RandomNormal(0, 1) → A51
  53. RandomNormal(0, 1) → A52
  54. RandomNormal(0, 1) → A53
  55. RandomNormal(0, 1) → A54
  56. RandomNormal(0, 1) → A55
  57. RandomNormal(0, 1) → A56
  58. RandomNormal(0, 1) → A57
  59. RandomNormal(0, 1) → A58
  60. RandomNormal(0, 1) → A59
  61. RandomNormal(0, 1) → A60
  62. RandomNormal(0, 1) → A61
  63. RandomNormal(0, 1) → A62
  64. RandomNormal(0, 1) → A63
  65. RandomNormal(0, 1) → A64
  66. RandomNormal(0, 1) → A65
  67. RandomNormal(0, 1) → A66
  68. RandomNormal(0, 1) → A67
  69. RandomNormal(0, 1) → A68
  70. RandomNormal(0, 1) → A69
  71. RandomNormal(0, 1) → A70
  72. RandomNormal(0, 1) → A71
  73. RandomNormal(0, 1) → A72
  74. RandomNormal(0, 1) → A73
  75. RandomNormal(0, 1) → A74
  76. RandomNormal(0, 1) → A75
  77. RandomNormal(0, 1) → A76
  78. RandomNormal(0, 1) → A77
  79. RandomNormal(0, 1) → A78
  80. RandomNormal(0, 1) → A79
  81. RandomNormal(0, 1) → A80
  82. RandomNormal(0, 1) → A81
  83. RandomNormal(0, 1) → A82
  84. RandomNormal(0, 1) → A83
  85. RandomNormal(0, 1) → A84
  86. RandomNormal(0, 1) → A85
  87. RandomNormal(0, 1) → A86
  88. RandomNormal(0, 1) → A87
  89. RandomNormal(0, 1) → A88
  90. RandomNormal(0, 1) → A89
  91. RandomNormal(0, 1) → A90
  92. RandomNormal(0, 1) → A91
  93. RandomNormal(0, 1) → A92
  94. RandomNormal(0, 1) → A93
  95. RandomNormal(0, 1) → A94
  96. RandomNormal(0, 1) → A95
  97. RandomNormal(0, 1) → A96
  98. RandomNormal(0, 1) → A97
  99. RandomNormal(0, 1) → A98
  100. RandomNormal(0, 1) → A99
  101. RandomNormal(0, 1) → A100
  102. DotPlot(list1, true) → list2
  103. CountIf(-1 < x < 0, list1) → b
  104. Sequence(CountIf[n < x < n + 1, list4], n, -3, 2) → list3
  105. LaTeX(list3, true, true) → text1
  106. Histogram({-5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5}, list4) → a

AI 绘图提示语参考

绘制一个正态分布统计模型。首先生成1000个符合标准正态分布的随机数据点，数据集中在0附近，两侧逐渐减少形成典型的钟形曲线。然后用直方图可视化这些数据的频数分布，直方图的柱子高度代表落在各个区间的数据个数。再用点图在同一坐标系中展示原始数据点的分布情况，直观呈现数据的离散程度。这个图形用于展示正态分布的特征，包括对称性、集中趋势和概率密度，适合教学演示中心极限定理和概率分布拟合。
以上提示语为根据原始绘图命令整理而来，仅供参考。