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Cumulative Frequency Polygon Demonstration

Cumulative Frequency Polygon Demonstration
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2012-11-26 17:33
PolygonSequenceProbability & StatisticsGeometric ConstructionGraphing
① This example demonstrates how to construct a cumulative frequency polygon, visualizing the cumulative distribution of a data set. ② Core concepts include cumulative frequency, frequency distribution, and polygon fitting in statistics. ③ Construction uses GeoGebra commands If, Sequence, PolyLine, Polygon, Point, Textfield, RotateText and objects such as yint2, xint2, A2, unitx, unity, list1, list2, poly1 to create vertices, axis scaling, and labels. ④ Suitable for high‑school statistics lessons, introductory university probability‑statistics courses, and teacher lesson‑plan references.

GeoGebra Commands & Parameters

  1. If(A3 - A2 > 0, A3 - A2, 5) → k
  2. Sequence((k * i, Element[list1, i]), i, 1, n) → list2
  3. PolyLine(list2) → a
  4. Polygon((unitx, 0.3), (unitx, -0.3), (2.5 * unitx, -0.3), (2.5 * unitx, 0.3)) → poly1, b, c, d, e
  5. Sequence(Segment[(xmin + xint2 * i, ymax), (xmin + xint2 * i, ymin)], i, 1, (xmax - xmin) / xint2) → list3
  6. Sequence(Segment[(xmin + xint1 * i, ymax), (xmin + xint1 * i, ymin)], i, 1, (xmax - xmin) / xint1) → list5
  7. Sequence(Segment[(xmin, ymin + yint1 * i), (xmax, ymin + yint1 * i)], i, 1, (ymax - ymin) / yint1) → list6
  8. Sequence(Segment[(xmin, ymin + yint2 * i), (xmax, ymin + yint2 * i)], i, 1, (ymax - ymin) / yint2) → list4
  9. Point(Segment[(k, 0), (n * k, 0)]) → P
  10. Point(Segment[(k, 0), (n * k, 0)]) → Q
  11. Point(Segment[(0, 0), (0, Element[list1, n])]) → P'
  12. Point(Segment[(0, 0), (0, Element[list1, n])]) → Q'
  13. PolyLine((unitx, 0), (1.5 * unitx, h), (2 * unitx, -h), (2.5 * unitx, 0)) → f
  14. Sequence(Segment[(k * i, 0), (k * i, (-h) / 3)], i, 1, n) → list7
  15. PolyLine(P, Intersect[x = x(P), a], P_1) → i
  16. PolyLine(P', Intersect[y = y(P'), a], P'_1) → l
  17. PolyLine(Q, Intersect[x = x(Q), a], Q_1) → j
  18. PolyLine(Q', Intersect[y = y(Q'), a], Q'_1) → m
  19. Textfield(xint2) → inputBox2
  20. Textfield(yint2) → inputBox3
  21. Textfield(text15) → inputBox5
  22. Textfield(text16) → inputBox4
  23. RotateText("Cumulative Frequency", 90*°) → text18