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Relationship between Histogram and Frequency Polygon

Relationship between Histogram and Frequency Polygon
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2016-10-24 08:47
Probability & StatisticsGeometric ConstructionGraphing
This example demonstrates how histograms and frequency polygons represent the same data distribution in different graphical forms. Key math concepts include data distribution, frequency, and geometric construction. GeoGebra commands/objects used are OrthogonalLine, Point, AttachCopyToView, Polygon, Midpoint, PolyLine, and Line, highlighting the process of transforming histogram data into a polygon. Suitable for high school mathematics education, focusing on statistical chart conversion and comparison.

GeoGebra Commands & Parameters

  1. OrthogonalLine(E_3, xAxis) → f_2
  2. Point(f_2) → A_3
  3. Point(f_2) → G_2
  4. AttachCopyToView(PolyLine[(NaN, NaN), (22.094214551897867, -0.05850817042635832), (22.094214551897867, -0.21819981491899154), (22.11364937414149, -0.33796854828846645), (22.133084196385116, -0.45773728165794136), (22.152519018628738, -0.5775060150274163), (22.152519018628738, -0.7371976595200495), (22.210823485359608, -0.8170434817663661), (22.230258307603233, -0.6573518372737328), (22.249693129846854, -0.5375831039042579), (22.288562774334103, -0.41781437053478304), (22.307997596577724, -0.29804563716530813), (22.32743241882135, -0.13835399267267492), (22.346867241064974, -0.018585259303200024), (22.366302063308595, 0.10118347406627488), (22.38573688555222, 0.22095220743574978), (22.405171707795844, 0.3407209408052247), (22.424606530039465, 0.4604896741746996), (22.44404135228309, 0.5802584075441745), (22.50234581901396, 0.6201813186673328), (22.521780641257582, 0.5004125852978579), (22.521780641257582, 0.3407209408052247), (22.541215463501207, 0.22095220743574978), (22.580085107988452, 0.10118347406627488), (22.599519930232077, -0.05850817042635832), (22.599519930232077, -0.21819981491899154), (22.638389574719323, -0.09843108154951663), (22.638389574719323, 0.06126056294311658), (22.657824396962948, 0.22095220743574978), (22.677259219206572, 0.10118347406627488), (22.696694041450193, -0.05850817042635832), true], 1, (12.84323916393311, -2.4538828378158564), (38.866466148144895, 19.902947391152793), (91.84771873479707, 525.4655286596177), (1430.8477187347983, -34.53447134038237)) → stroke1
  5. Point(xAxis) → B_3
  6. Point(xAxis) → H_2
  7. Point(xAxis) → J_2
  8. Point(xAxis) → K
  9. Point(xAxis) → L
  10. Point(xAxis) → M
  11. Point(xAxis) → N
  12. Point(xAxis) → O
  13. Point(xAxis) → P
  14. Point(xAxis) → Q
  15. Polygon(B_3, R, S, H_2) → poly1, b_1, r, s, h
  16. Point(s) → T
  17. Polygon(H_2, T, U, J_2) → poly2, h_1, t, u, j
  18. Polygon(J_2, V, W, K) → poly3, j_1, v, w, k_2
  19. Point(w) → Z
  20. Polygon(K, Z, A_1, L) → poly4, k_1, z_1, a_1, l
  21. Point(a_1) → B_1
  22. Polygon(L, B_1, C_1, M) → poly5, l_1, b_2, c_1, m_1
  23. Polygon(M, D_1, E_1, N) → poly6, m_2, d_1, e_1, n_1
  24. Polygon(N, E_1, F_1, O) → poly7, n_2, e_2, f_1, o
  25. Point(f_1) → G_1
  26. Polygon(O, G_1, H_1, P) → poly8, o_1, g_1, h_2, p_1
  27. Polygon(H_1, I_1, Q, P) → poly9, h_3, i_1, q_1, p_2
  28. Midpoint(r) → J_1
  29. Midpoint(v) → K_1
  30. Midpoint(t) → L_1
  31. Midpoint(z_1) → M_1
  32. Midpoint(b_2) → N_1
  33. Midpoint(d_1) → O_1
  34. Midpoint(e_2) → P_1
  35. Midpoint(g_1) → Q_1
  36. Midpoint(h_3) → R_1
  37. Point(xAxis) → S_1
  38. Point(xAxis) → J
  39. PolyLine(S_1, J_1, J, L_1, K_1, M_1, N_1, O_1, P_1, Q_1, R_1) → g
  40. Midpoint(B_3, H_2) → A
  41. Midpoint(H_2, J_2) → B
  42. Midpoint(J_2, K) → C
  43. Midpoint(K, L) → D
  44. Midpoint(L, M) → E
  45. Midpoint(M, N) → F
  46. Midpoint(N, O) → G
  47. Midpoint(O, P) → H
  48. Midpoint(P, Q) → I
  49. Point(xAxis) → T_1
  50. Point(xAxis) → U_1
  51. Line(T_1, U_1) → i