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Histogram Construction Tool: Frequency Counting and Distribution Parameters

Histogram Construction Tool: Frequency Counting and Distribution Parameters
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2020-09-02 17:02
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This example demonstrates how to automatically build a histogram in GeoGebra and visualize how the distribution shape emerges from frequency counts over integer values. Key concepts include histogram binning, frequency/statistical counting, and a discrete probability model (notably the binomial distribution) with parameters such as p and q, along with integer sample ranges. Construction-wise, the workflow determines the value bounds with Length, Min, and Max, then uses If together with CountIf to select and count data falling into each bin. Sequence is used to generate the required indices/integer values for binning, and Frequency aggregates the resulting counts. For presentation, Textfield and TableText manage labels and tabular outputs, while Append assembles the display elements. Finally, Segment and VerticalText are used to draw the vertical bars of the histogram and annotate them. Suitable for upper-secondary through early university probability & statistics, classroom demonstrations, and interactive exploration of how parameter changes affect empirical frequency patterns.

GeoGebra Commands & Parameters

  1. Length(Data) → n
  2. Min(Data) → p
  3. Max(Data) → q
  4. If(d > 1, 1, If[d > 0.1, 0.1, 0.01]) → t
  5. CountIf(A2 ≤ x ≤ C2, Data) → H2
  6. CountIf(A3 ≤ x ≤ C3, Data) → H3
  7. CountIf(A4 ≤ x ≤ C4, Data) → H4
  8. CountIf(A5 ≤ x ≤ C5, Data) → H5
  9. CountIf(A6 ≤ x ≤ C6, Data) → H6
  10. CountIf(A7 ≤ x ≤ C7, Data) → H7
  11. CountIf(A8 ≤ x ≤ C8, Data) → H8
  12. CountIf(A9 ≤ x ≤ C9, Data) → H9
  13. Sequence(a - t / 2 + ((i - 1) * d), i, 1, k + 1, 1) → Boundaries
  14. Frequency(Boundaries, Data) → Freq
  15. Max(ceil(Max[Freq] / b), 2) → u
  16. Sequence(a - t / 2 + (((2 * i) - 1) * d / 2), i, 1, k, 1) → ClassMark
  17. Sequence((i * b), i, 2, u + 1, 2) → FreqMark
  18. Sequence((-8.5 - (0.25 * (ceil(lg(Element[FreqMark, i / 2] + 1)) - 1)), i - 4.15), i, 2, u + 1, 2) → Ypoint
  19. Sequence((i - 8.15 - (0.15 * ceil(lg(Element[ClassMark, (i - 1) / 2] + 1) - 1)), -4.6), i, 3, 2 + (2 * k) - 1, 2) → Xpoint
  20. Textfield(Title) → InputBoxTitle
  21. Textfield(Data) → InputBoxData
  22. Textfield(a) → InputBox3
  23. Sequence(If[n ≥ i, Element[Data, i], x], i, 1, If[n ≥ 10, 10, n], 1) → list1
  24. Sequence(If[n ≥ i, Element[Data, i], x], i, 11, If[n ≥ 20, 20, n], 1) → list2
  25. Sequence(If[n ≥ i, Element[Data, i], 32], i, 21, If[n ≥ 30, 30, n], 1) → list3
  26. Sequence(If[n ≥ i, Element[Data, i], x], i, 31, If[n ≥ 40, 40, n], 1) → list4
  27. Sequence(If[n ≥ i, Element[Data, i], x], i, 51, If[n ≥ 60, 60, n], 1) → list6
  28. Sequence(If[n ≥ i, Element[Data, i], x], i, 61, If[n ≥ 70, 70, n], 1) → list7
  29. Sequence(If[n ≥ i, Element[Data, i], x], i, 71, If[n ≥ 80, 80, n], 1) → list8
  30. Sequence(If[n ≥ i, Element[Data, i], x], i, 81, If[n ≥ 90, 90, n], 1) → list9
  31. Sequence(If[n ≥ i, Element[Data, i], x], i, 41, If[n ≥ 50, 50, n], 1) → list5
  32. Sequence(If[n ≥ i, Element[Data, i], x], i, 91, If[n ≥ 100, 100, n], 1) → list10
  33. TableText({list1, list2, list3, list4, list5, list6, list7, list8, list9, list10, "."}) → text21
  34. Append(Element[list11, 1], Sequence[Element[list21, i], i, 1, k, 1]) → list25
  35. Append(Element[list11, 2], Sequence[Element[list22, i], i, 1, k, 1]) → list26
  36. Append(Element[list11, 3], Sequence[Element[list23, i], i, 1, k, 1]) → list27
  37. Append(Element[list11, 4], Sequence[Element[list24, i], i, 1, k, 1]) → list28
  38. TableText({list25, list26, list27, list28}, "vc|_") → text22
  39. Sequence(Segment[(-8, (0.2 * i) - 4), (-5 + (2 * k), (0.2 * i) - 4)], i, 1, ((u + 1) * 5), 1) → Hori1
  40. Sequence(Segment[(-8, i - 4), (-5 + (2 * k), i - 4)], i, 0, u + 1, 1) → Hori2
  41. Segment((-7.2, -3.6), (-7, -4.4)) → h
  42. Segment((-7.4, -4), (-7.2, -3.6)) → g
  43. Segment((-8.2, -4), (-7.4, -4)) → f
  44. Segment((-8, -4), (-8, u - 3)) → Yaxis
  45. Segment((-6.8, -4), (-5 + (2 * k), -4)) → Xaxis
  46. Segment((-7, -4.4), (-6.8, -4)) → i
  47. Sequence(Segment[(-8, i - 4), (-8.2, i - 4)], i, 2, u + 1, 2) → Hori3
  48. Sequence(Segment[(i - 8, -4), (i - 8, u - 3)], i, 1, 2 + (2 * k) + 1, 1) → Vert2
  49. Sequence(Segment[(i - 8, -4), (i - 8, -4.2)], i, 3, 2 + (2 * k) - 1, 2) → Vert3
  50. Sequence(Polygon[(-6 + (2 * (i - 1)), -4), (-6 + (2 * (i - 1)), -4 + Element[Freq, i] / b), (-6 + (2 * i), -4 + Element[Freq, i] / b), (-6 + (2 * i), -4)], i, 1, k, 1) → Block
  51. Sequence(Segment[((0.2 * i) - 8, -4), ((0.2 * i) - 8, u - 3)], i, 1, ((2 + (2 * k) + 1) * 5), 1) → Vert1
  52. VerticalText(If[chi ≟ true, "頻 數", "Frequency"]) → text17

AI Drawing Prompt Reference

Draw a histogram showing frequency distribution of data. Determine data range from min and max, generate intervals via sequence, count frequencies per bin, then draw vertical bars with heights equal to frequencies. Label intervals and frequencies on the left, and annotate the right. Construction order: set range and bin width, count frequencies, then draw bars and labels.
The prompt above was compiled from the original drawing commands and is for reference only.