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From Histograms to Frequency Polygons by Elen

From Histograms to Frequency Polygons by Elen
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2020-02-26 17:12
PolygonIntegralProbability & Statistics
This example demonstrates how to draw a frequency polygon from a histogram and shows how the area enclosed by the frequency polygon relates to the total area. It involves core math concepts like histograms, frequency polygons, functions, 2D vectors, general quadrilaterals, diagrams, and definite integrals. The construction uses GeoGebra commands/objects such as If, Point, Midpoint, CountIf, Polygon, PolyLine, Sequence, Textfield, Segment, and RotateText. Suitable for high school mathematics teaching, particularly in probability & statistics and introductory calculus.

GeoGebra Commands & Parameters

  1. If(C2 - A2 > 0, C2 - A2 + A3 - C2, 5) → k
  2. Point(Ray[(10 * k, 0), (10 * k, 1)]) → Q10
  3. Point(Ray[(9 * k, 0), (9 * k, 1)]) → Q9
  4. Midpoint(Q10, Q9) → M9
  5. Point(Ray[(8 * k, 0), (8 * k, 1)]) → Q8
  6. Midpoint(Q8, Q9) → M8
  7. Point(Ray[(7 * k, 0), (7 * k, 1)]) → Q7
  8. Midpoint(Q8, Q7) → M7
  9. Point(Ray[(6 * k, 0), (6 * k, 1)]) → Q6
  10. Midpoint(Q6, Q7) → M6
  11. Point(Ray[(5 * k, 0), (5 * k, 1)]) → Q5
  12. Midpoint(Q6, Q5) → M5
  13. Point(Ray[(4 * k, 0), (4 * k, 1)]) → Q4
  14. Midpoint(Q4, Q5) → M4
  15. Point(Ray[(3 * k, 0), (3 * k, 1)]) → Q3
  16. Midpoint(Q3, Q4) → M3
  17. Point(Ray[(2 * k, 0), (2 * k, 1)]) → Q2
  18. Midpoint(Q2, Q3) → M2
  19. Point(Ray[(k, 0), (k, 1)]) → Q1
  20. Midpoint(Q1, Q2) → M1
  21. CountIf(x ≠ " ", list7) → n
  22. Polygon((unitx, 0.3), (unitx, -0.3), (2.5 * unitx, -0.3), (2.5 * unitx, 0.3)) → poly1, a, b, c, d
  23. PolyLine((unitx, 0), (1.5 * unitx, h), (2 * unitx, -h), (2.5 * unitx, 0)) → e
  24. Sequence(Segment[(xmin + xint2 * i, ymax), (xmin + xint2 * i, ymin)], i, 1, (xmax - xmin) / xint2) → list3
  25. Sequence(Segment[(xmin, ymin + yint2 * i), (xmax, ymin + yint2 * i)], i, 1, (ymax - ymin) / yint2) → list4
  26. Sequence(Sequence[Segment[(xint2 * (j - 1) + xint1 * i, ymax), (xint2 * (j - 1) + xint1 * i, ymin)], i, 1, 4], j, 1, ceil(xmax / xint2)) → list5
  27. Sequence(Sequence[Segment[(xmin, (j - 1) * yint2 + yint1 * i), (xmax, (j - 1) * yint2 + yint1 * i)], i, 1, 4], j, 1, ceil(ymax / yint2)) → list6
  28. Sequence(Segment[(k * i + 0.5 * k, 0), (k * i + 0.5 * k, (-h) / 2.5)], i, 1, n - 1) → list9
  29. Sequence(Segment[(k * i, 0), (k * i, (-h) / 2.5)], i, 1, n) → list8
  30. Textfield(text23) → inputBox2
  31. Textfield(text24) → inputBox4
  32. Textfield(xint1') → inputBox3
  33. Sequence(Polygon[((i - 0.5) * k, 0), ((i + 0.5) * k, 0), ((i + 0.5) * k, Element[list1, i]), ((i - 0.5) * k, Element[list1, i])], i, 1, n) → list2
  34. Segment(Q1, Q2) → l1
  35. Segment(Q2, Q3) → l2
  36. Segment(Q3, Q4) → l3
  37. Segment(Q4, Q5) → l4
  38. Segment(Q5, Q6) → l5
  39. Segment(Q6, Q7) → l6
  40. Segment(Q7, Q8) → l7
  41. Segment(Q8, Q9) → l8
  42. Segment(Q9, Q10) → l9
  43. Sequence(If[y(Element[list10, i]) > y(Element[list11, i - 1]), Rotate[Polygon[Element[list10, i], Element[list11, i - 1], Element[list10, i] - (0.5 * k, 0)], t, Element[list11, i - 1]], Polygon[Element[list10, i], Element[list10, i] - (0.5 * k, 0), Element[list10, i]]], i, 2, n) → list2_3
  44. Sequence(If[y(Element[list10, i]) < y(Element[list11, i]), Polygon[Element[list10, i], Element[list10, i] - (0, y(Element[list10, i])), Element[list10, i] - (-0.5 * k, y(Element[list10, i])), Element[list10, i] + (0.5 * k, 0)], Polygon[Element[list10, i], Element[list11, i], Element[list11, i] - (0, y(Element[list11, i])), Element[list10, i] - (0, y(Element[list10, i]))]], i, 1, n - 1) → list2_2
  45. Sequence(If[y(Element[list11, i]) < y(Element[list10, i + 1]), Polygon[Element[list11, i], Element[list10, i + 1], Element[list10, i + 1] - (0, y(Element[list10, i + 1])), Element[list11, i] - (0, y(Element[list11, i]))], Polygon[Element[list10, i + 1], Element[list10, i + 1] - (k / 2, 0), Element[list10, i + 1] - (k / 2, y(Element[list10, i + 1])), Element[list10, i + 1] - (0, y(Element[list10, i + 1]))]], i, 1, n) → list2_1
  46. Sequence(If[y(Element[list10, i]) > y(Element[list11, i]), Rotate[Polygon[Element[list10, i], Element[list11, i], Element[list10, i] + (0.5 * k, 0)], -t, Element[list11, i]], Polygon[Element[list10, i], Element[list10, i] + (0.5 * k, 0), Element[list10, i]]], i, 1, n - 1) → list2_4
  47. Polygon(Q1, Q1 - (0.5 * k, 0), Q1 - (0.5 * k, y(Q1)), (x(Q1), 0)) → poly2, q1, f, i, j
  48. Polygon(Element[list10, n], (x(Element[list10, n]), 0), (x(Element[list10, n]) + 0.5 * k, 0), Element[list10, n] + (0.5 * k, 0)) → poly3, l, m, p, q
  49. RotateText("Frequency", 90*°) → text12