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频数分布表构建工具

频数分布表构建工具
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2020-09-02 16:44
函数数列概率统计
① 本范例演示如何在 GeoGebra 中自动生成频数分布表，直观展示数据分组与频数统计的过程。② 涉及的核心数学概念包括频数分布、区间划分、频数计算、数据汇总等统计基础知识。③ 作图要点：使用 Max、Min、Sequence、Unique、CountIf、Frequency、Sum、Length、If、Append、TableText、Textfield、RotateText、Segment 等命令，配合对象 chi、NumClasses、ClassLimit1、Data、q、ClassWidth、A2‑A13、t、C2‑C12、H2‑H12 实现动态分组与表格生成。④ 适用于高中统计课程、大学概率统计入门教学以及数据分析演示，可作为教学演示或学生自主探索的交互式工具。

GeoGebra 命令及参数

  1. Max(Data) → q
  2. If(ClassWidth > 1, 1, If[ClassWidth > 0.1, 0.1, 0.01]) → t
  3. CountIf(A2 ≤ x ≤ C2, Data) → H2
  4. CountIf(A3 ≤ x ≤ C3, Data) → H3
  5. CountIf(A4 ≤ x ≤ C4, Data) → H4
  6. CountIf(A5 ≤ x ≤ C5, Data) → H5
  7. CountIf(A6 ≤ x ≤ C6, Data) → H6
  8. CountIf(A7 ≤ x ≤ C7, Data) → H7
  9. CountIf(A8 ≤ x ≤ C8, Data) → H8
  10. CountIf(A9 ≤ x ≤ C9, Data) → H9
  11. CountIf(A10 ≤ x ≤ C10, Data) → H10
  12. CountIf(A11 ≤ x ≤ C11, Data) → H11
  13. CountIf(A12 ≤ x ≤ C12, Data) → H12
  14. CountIf(A13 ≤ x ≤ C13, Data) → H13
  15. Length(Data) → NumData
  16. Min(Data) → p
  17. Sequence(ClassLimit1 - t / 2 + (((2 * i) - 1) * ClassWidth / 2), i, 1, NumClasses, 1) → ClassMark
  18. Sequence((i - 8.15 - (0.15 * ceil(lg(Element[ClassMark, (i - 1) / 2] + 1) - 1)), -4.6), i, 3, 2 + (2 * NumClasses) - 1, 2) → Xpoint
  19. RotateText("Frequency", 90°) → text17
  20. Textfield(Data) → InputBox2
  21. Textfield(ClassLimit1) → InputBox3
  22. Sequence(If[NumData ≥ i, Element[Data, i], x], i, 1, If[NumData ≥ 10, 10, NumData], 1) → DataRow1
  23. Sequence(If[NumData ≥ i, Element[Data, i], x], i, 11, If[NumData ≥ 20, 20, NumData], 1) → DataRow2
  24. Sequence(If[NumData ≥ i, Element[Data, i], 32], i, 21, If[NumData ≥ 30, 30, NumData], 1) → DataRow3
  25. Sequence(If[NumData ≥ i, Element[Data, i], x], i, 31, If[NumData ≥ 40, 40, NumData], 1) → DataRow4
  26. Sequence(If[NumData ≥ i, Element[Data, i], x], i, 51, If[NumData ≥ 60, 60, NumData], 1) → DataRow6
  27. Sequence(If[NumData ≥ i, Element[Data, i], x], i, 41, If[NumData ≥ 50, 50, NumData], 1) → DataRow5
  28. If(chi ≟ true, {"組別", "組界", "組中點", "頻數"}, {"Group", "Class boundaries", "Class mark", "Frequency"}) → ColumnHeads
  29. Append(Element[ColumnHeads, 1], Sequence[Element[Classes, i], i, 1, NumClasses, 1]) → TableList1
  30. Append(Element[ColumnHeads, 2], Sequence[Element[Boundaries, i], i, 1, NumClasses, 1]) → TableList2
  31. Append(Element[ColumnHeads, 3], Sequence[Element[ClassMarks, i], i, 1, NumClasses, 1]) → TableList3
  32. Append(Element[ColumnHeads, 4], Sequence[Element[Frequencies, i], i, 1, NumClasses, 1]) → TableList4
  33. Segment((-7.2, -3.6), (-7, -4.4)) → h
  34. Segment((-7.4, -4), (-7.2, -3.6)) → g
  35. Segment((-8.2, -4), (-7.4, -4)) → f
  36. Segment((-6.8, -4), (-5 + (2 * NumClasses), -4)) → Xaxis
  37. Segment((-7, -4.4), (-6.8, -4)) → i
  38. Sequence(Segment[(i - 8, -4), (i - 8, -4.2)], i, 3, 2 + (2 * NumClasses) - 1, 2) → TicksVert3
  39. TableText({TableList1, TableList4}, "vc|_") → text22
  40. TableText({DataRow1, DataRow2, DataRow3, DataRow4, DataRow5, DataRow6, "."}) → text21
  41. Unique(Data) → Items
  42. If(chi ≟ true, {"-- 請選擇 --", "分組", "不分組"}, {"-- please select --", "in groups", "without grouping"}) → Option
  43. Length(Items) → NumItems
  44. Sum(Data) → c
  45. Sum(DataFloor) → d
  46. If(c ≠ d, Max[0.1, floor(((q - ClassLimit1) / NumClasses * 10)) / 10], ceil((q - ClassLimit1 + 1) / NumClasses)) → r
  47. If(c ≠ d, Max[0.1, (q - ClassLimit1) / (NumClasses - 1)], Max[r + 1, ceil((q - ClassLimit1) / (NumClasses - 1))]) → s
  48. Frequency(Data) → FreqItems
  49. Append(If[chi ≟ true, "項目", "Item"], Sequence[Element[Items, i], i, 1, NumItems, 1]) → TableListItems
  50. Append(If[chi ≟ true, "頻數", "Frequency"], Sequence[Element[FreqItems, i], i, 1, NumItems, 1]) → TableListFreqItems
  51. TableText({TableListItems, TableListFreqItems}, "vc|_") → text3

AI 绘图提示语参考

创建一个动态频数分布表工具，允许用户输入原始数据、设定分组起始值和组数，自动计算最大值、最小值、组距、组中点与各组频数，并在界面上显示分组表、原始数据列表以及坐标轴刻度，支持中英文切换。
以上提示语为根据原始绘图命令整理而来，仅供参考。