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均值、中位数与众数的动态可视化演示

均值、中位数与众数的动态可视化演示
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2018-02-27 10:36
角函数概率统计滑块动画函数图像
该范例通过GeoGebra动态展示一组随机数据的均值（mean）、中位数（median）与众数（mode）的计算与图形表示。核心数学概念是描述性统计中的集中趋势度量，涉及数据排序、频率分布以及茎叶图、点图、箱线图等多种统计图表。作图要点包括使用Random命令生成随机数据，Sum计算总和，Median、Mode、Q1、Q3、Min、Max等统计函数提取关键值，并通过StemPlot、DotPlot、BoxPlot绘制数据分布；同时利用Circle、Rotate、Angle、CircleSector等几何对象构建单位圆与角度可视化，配合Textfield和LaTeX输入框实现交互式参数调整。适合中学数学统计模块教学，帮助学生直观理解不同统计量对数据集中趋势的刻画差异，以及异常值对均值与中位数的影响。

GeoGebra 命令及参数

  1. Random(1, 5) → B2
  2. Random(1, 5) → B3
  3. Random(1, 5) → B4
  4. Random(1, 5) → B5
  5. Sum(B2:B5) → B6
  6. Random(26, 29) → A11
  7. Random(26, 29) → A12
  8. Random(26, 29) → A13
  9. Random(26, 29) → A14
  10. Random(26, 29) → A15
  11. Random(26, 32) → A16
  12. Random(26, 33) → A17
  13. Random(29, 35) → B11
  14. Random(30, 35) → B13
  15. Random(30, 35) → B14
  16. Random(30, 35) → B16
  17. Random(30, 35) → B18
  18. Random(28, 35) → A18
  19. Random(29, 35) → B12
  20. Random(28, 35) → B15
  21. Random(28, 35) → B17
  22. Random(35, 42) → C11
  23. Random(35, 42) → C12
  24. Random(35, 42) → C13
  25. Random(35, 42) → C14
  26. Random(35, 42) → C15
  27. Random(35, 42) → C17
  28. Random(35, 42) → C18
  29. Random(37, 43) → D11
  30. Random(33, 43) → D12
  31. Random(37, 44) → D13
  32. Random(40, 44) → D14
  33. Random(40, 44) → D15
  34. Random(40, 44) → D16
  35. Random(40, 44) → D17
  36. Random(40, 43) → D18
  37. Random(35, 42) → C16
  38. StemPlot({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → text11
  39. DotPlot({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → list4
  40. BoxPlot(1, 1, {A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}, true) → b
  41. Q3({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → i
  42. Q1({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → h
  43. Min({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → B19
  44. Max({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → A19
  45. Mode({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → D10
  46. Median({A11, A12, A13, A14, A15, A16, A17, A18, B11, B12, B13, B14, B15, B16, B17, B18, C11, C12, C13, C14, C15, C16, C17, C18, D11, D12, D13, D14, D15, D16, D17, D18}) → C10
  47. Mode(B2:B5) → A9
  48. Min(B2:B5) → A7
  49. Max(B2:B5) → A6
  50. Median({B2, B3, B4, B5}) → B8
  51. Ordinal(Median[A2:A5, B2:B5]) → B9
  52. TableText({{A1, B1}, {A2, B2}, {A3, B3}, {A4, B4}, {A5, B5}}, "c_|") → text8
  53. Circle(A, B) → c
  54. Rotate(B, D2, A) → B'
  55. Angle(B, A, B') → α
  56. Rotate(B', D3, A) → B''
  57. Angle(B', A, B'') → β
  58. Rotate(B'', D4, A) → B'''
  59. Angle(B'', A, B''') → γ
  60. CircleSector(A, B', B'') → d
  61. CircleSector(A, B, B') → e
  62. CircleSector(A, B''', B) → f
  63. CircleSector(A, B'', B''') → g
  64. TableText({{A1, A2, A3, A4, A5}, {B1, B2, B3, B4, B5}}, "c_|") → text10
  65. Element(list3, a) → j
  66. Textfield(text33) → inputBox2
  67. LaTeX(right, true, true) → text36
  68. LaTeX(wrong, true, true) → text37
  69. Textfield(Name) → inputBox1
  70. Element(list2, a) → text20

AI 绘图提示语参考

绘制一组随机数据的统计图表，包括茎叶图、点图和箱线图。首先生成一组随机数据，然后计算这些数据的中位数、四分位数、最小值、最大值和众数。接着绘制茎叶图、点图和箱线图来展示数据分布，并在图中显示这些统计值。
以上提示语为根据原始绘图命令整理而来，仅供参考。