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Area Histograms: Choose Your Zones

Area Histograms: Choose Your Zones
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2017-05-07 17:28
CalculusIntegralProbability & Statistics
This example demonstrates area histograms by selecting different zones. Key mathematical concepts include area calculation, histogram in statistics, and integral calculus. Using GeoGebra commands such as Append, Insert, and Point, a dynamic area histogram can be constructed. Suitable for high school and above students or teachers for teaching and learning.

GeoGebra Commands & Parameters

  1. Append(dividerlist, 10) → barrights
  2. Insert(0, dividerlist, 1) → barlefts
  3. Point(Segment[(0, pointheight), (10, pointheight)]) → A1
  4. Point(Segment[(0, pointheight), (10, pointheight)]) → A2
  5. Point(Segment[(0, pointheight), (10, pointheight)]) → A3
  6. Point(Segment[(0, pointheight), (10, pointheight)]) → A4
  7. Point(Segment[(0, pointheight), (10, pointheight)]) → A5
  8. Point(Segment[(0, pointheight), (10, pointheight)]) → A6
  9. Point(Segment[(0, pointheight), (10, pointheight)]) → A7
  10. Point(Segment[(0, pointheight), (10, pointheight)]) → A8
  11. Point(Segment[(0, pointheight), (10, pointheight)]) → A9
  12. Point(Segment[(0, pointheight), (10, pointheight)]) → A10
  13. Point(Segment[(0, pointheight), (10, pointheight)]) → A11
  14. Point(Segment[(0, pointheight), (10, pointheight)]) → A12
  15. Point(Segment[(0, pointheight), (10, pointheight)]) → A13
  16. Point(Segment[(0, pointheight), (10, pointheight)]) → A14
  17. Point(Segment[(0, pointheight), (10, pointheight)]) → A15
  18. Point(Segment[(0, pointheight), (10, pointheight)]) → A16
  19. Point(Segment[(0, pointheight), (10, pointheight)]) → A17
  20. Point(Segment[(0, pointheight), (10, pointheight)]) → A18
  21. Point(Segment[(0, pointheight), (10, pointheight)]) → A19
  22. Point(Segment[(0, pointheight), (10, pointheight)]) → A20
  23. Point(Segment[(0, pointheight), (10, pointheight)]) → A21
  24. Point(Segment[(0, pointheight), (10, pointheight)]) → A22
  25. Point(Segment[(0, pointheight), (10, pointheight)]) → A23
  26. Point(Segment[(0, pointheight), (10, pointheight)]) → A24
  27. Point(Segment[(0, pointheight), (10, pointheight)]) → A25
  28. Point(Segment[(0, pointheight), (10, pointheight)]) → A26
  29. Point(Segment[(0, pointheight), (10, pointheight)]) → A27
  30. Point(Segment[(0, pointheight), (10, pointheight)]) → A28
  31. Point(Segment[(0, pointheight), (10, pointheight)]) → A29
  32. Point(Segment[(0, pointheight), (10, pointheight)]) → A30
  33. Point(xAxis) → B1
  34. Point(xAxis) → B2
  35. Point(xAxis) → B3
  36. Point(xAxis) → B4
  37. Point(xAxis) → B5
  38. Point(xAxis) → B6
  39. Point(xAxis) → B7
  40. Point(xAxis) → B8
  41. Point(xAxis) → B9
  42. Point(xAxis) → B10
  43. Length(dividerlist) → numdividers
  44. Zip(Sum[(x(A1:A30) ≥ L) ∧ (x(A1:A30) < R)], L, barlefts, R, barrights) → barcounts
  45. Sum(barcounts) → a
  46. Zip(R - L, L, barlefts, R, barrights) → barwidths
  47. Sum(barwidths) → b
  48. Zip(Polygon[{(L, 0), (L, H), (R, H), (R, 0)}], L, barlefts, R, barrights, H, barheights) → bars
  49. Sum(bars) → c
  50. Zip(Segment[(L, -0.5), (L, -1)], L, Append[barlefts, 10]) → list1
  51. Zip(Zip[Segment[(L, (H / N * j)), (R, (H / N * j))], j, Sequence[N]], L, barlefts, R, barrights, H, barheights, N, barcounts) → bardividers