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Histogram with Unequal Class Intervals

Histogram with Unequal Class Intervals
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2015-09-18 21:24
FunctionProbability & StatisticsGraphing
This GeoGebra example demonstrates how to create a histogram with unequal class intervals. Unlike equal-width histograms, the height of each bar in an unequal-interval histogram represents frequency density (frequency divided by class width), which accurately reflects the data distribution. Key mathematical concepts include frequency density, class width, and frequency distribution. Construction uses Sequence to generate multiple bars of varying widths, Point/Line/Segment to define bar vertices, Polygon to form closed bar regions, and lists to manage data. Suitable for secondary school statistics teaching and university-level probability courses.

GeoGebra Commands & Parameters

  1. OrthogonalLine(S, y = 0) → l_1
  2. Point(l_1) → Z
  3. Point(xAxis) → A
  4. Point(xAxis) → B
  5. Line(A, B) → k_1
  6. Point(xAxis) → C
  7. Point(xAxis) → D
  8. Point(xAxis) → E
  9. Point(xAxis) → F
  10. Sequence((x(G), y(G) - (10 * i)), i, 1, 6) → liste1
  11. Sequence((x(H), y(H) - (10 * i)), i, 1, 6) → liste2
  12. Sequence((x(I), y(I) - (10 * i)), i, 1, 6) → liste3
  13. Sequence((x(J), y(J) - (10 * i)), i, 1, 6) → liste4
  14. Sequence((x(K), y(K) - (10 * i)), i, 1, 6) → liste5
  15. Point(liste1) → L
  16. Segment(G, L) → a
  17. Point(liste2) → M
  18. Segment(H, M) → b
  19. Point(liste3) → N
  20. Segment(I, N) → c
  21. Point(liste4) → O
  22. Segment(J, O) → d
  23. Point(liste5) → P
  24. Segment(K, P) → e
  25. Sequence(Segment[(x(G), y(G) - (10 * i)), (x(G) + 60, y(G) - (10 * i))], i, 0, 6) → liste6
  26. Sequence(Segment[(x(G) + 90, y(G) - (10 * i)), (x(G) + 60, y(G) - (10 * i))], i, 0, 6) → liste7
  27. Vector(S, Z) → u
  28. Polygon(A, B, (x(B), ((f * 0.1) * y(V))), (x(A), ((f * 0.1) * y(V)))) → poly1, p, q, r, s
  29. Polygon(B, C, (x(C), ((g * 0.1) * y(V))), (x(B), ((g * 0.1) * y(V)))) → poly2, t, a_1, b_1, c_1
  30. Polygon(C, D, (x(D), ((h * 0.1) * y(V))), (x(C), ((h * 0.1) * y(V)))) → poly3, d_1, e_1, f_1, m_1
  31. Polygon(D, E, (x(E), ((i * 0.1) * y(V))), (x(D), ((i * 0.1) * y(V)))) → poly4, g_1, h_1, n_1, p_1
  32. Polygon(E, F, (x(F), ((j * 0.1) * y(V))), (x(E), ((j * 0.1) * y(V)))) → poly5, i_1, j_1, q_1, r_1
  33. Point(l_1) → W
  34. Vector(S, W) → v
  35. Polygon(A, B, (x(B), (h1 * y(E_1))), (x(A), (h1 * y(E_1)))) → poly6, s_1, t_1, a_2, b_2
  36. Polygon(B, C, (x(C), (h2 * y(E_1))), (x(B), (h2 * y(E_1)))) → poly7, b_3, c_2, d_2, e_2
  37. Polygon(C, D, (x(D), (h3 * y(E_1))), (x(C), (h3 * y(E_1)))) → poly8, c_3, d_3, f_2, g_2
  38. Polygon(D, E, (x(E), (h4 * y(E_1))), (x(D), (h4 * y(E_1)))) → poly9, d_4, e_3, h_2, i_2
  39. Polygon(E, F, (x(F), (h5 * y(E_1))), (x(E), (h5 * y(E_1)))) → poly10, e_4, f_3, j_2, k_2

AI Drawing Prompt Reference

Draw a histogram with unequal class intervals on a coordinate plane. Place six points sequentially on the x-axis to define five intervals of varying widths. For each interval, construct a rectangle whose base is the interval and whose height equals the frequency divided by the class width, representing frequency density. Use polygons to form five closed rectangular bars with different widths but heights calculated precisely from frequency density values. The area of each bar accurately reflects the frequency distribution. The resulting statistical histogram is suitable for teaching probability and data distribution concepts.
The prompt above was compiled from the original drawing commands and is for reference only.