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Distribution Comparison

Distribution Comparison
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2014-09-25 13:51
Probability & StatisticsOptimizationGraphing
In collections Statistical Intuition Builders
This example demonstrates how to compare and contrast statistical measures of center (like mean, median) and data displays (like box plots, scatter plots) across different datasets. It visually illustrates concepts such as normal distribution and standard deviation through dynamic manipulation. Key construction elements include commands like Polygon, PointIn, BoxPlot, MeanX, SDX, Normal, Intersect, Circle, OrthogonalLine, Segment, Mirror, and objects like poly1, a, top, c, mid, etc. Suitable for high school and above mathematics education, particularly in probability & statistics and data analysis courses.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C, D) → poly1, a, top, c, mid
  2. Polygon(E, F, G, H) → poly2, e, bottom, g, h
  3. PointIn(poly1) → P
  4. PointIn(poly1) → Q
  5. PointIn(poly1) → R
  6. PointIn(poly1) → O
  7. PointIn(poly1) → A_1
  8. PointIn(poly1) → B_1
  9. PointIn(poly1) → I
  10. PointIn(poly1) → J
  11. PointIn(poly1) → K
  12. PointIn(poly1) → L
  13. PointIn(poly1) → M
  14. PointIn(poly1) → N
  15. PointIn(poly2) → S
  16. PointIn(poly2) → T
  17. PointIn(poly2) → U
  18. PointIn(poly2) → V
  19. PointIn(poly2) → W
  20. PointIn(poly2) → Z
  21. PointIn(poly2) → C_1
  22. PointIn(poly2) → D_1
  23. PointIn(poly2) → E_1
  24. PointIn(poly2) → F_1
  25. PointIn(poly2) → G_1
  26. PointIn(poly2) → H_1
  27. BoxPlot(7.5, 0.3, x(list_o), true) → boxorange
  28. BoxPlot(6.5, 0.3, x(list_p), true) → boxpurple
  29. MeanX(list_o) → mean_o
  30. MeanX(list_p) → mean_p
  31. SDX(list_o) → sd_o
  32. SDX(list_p) → sd_p
  33. Normal(mean_o, sd_o, x) → f
  34. Normal(mean_p, sd_p, x) → p
  35. Intersect(d, xAxis) → I_1
  36. Intersect(b, xAxis) → J_1
  37. Circle(I_1, sd_p) → k
  38. Circle(I_1, (2 * sd_p)) → s
  39. Circle(I_1, (3 * sd_p)) → t
  40. Circle(J_1, sd_o) → c_1
  41. Circle(J_1, (2 * sd_o)) → d_1
  42. Circle(J_1, (3 * sd_o)) → e_1
  43. Intersect(k, xAxis) → K_1, L_1
  44. Intersect(s, xAxis) → M_1, N_1
  45. Intersect(t, xAxis) → O_1, P_1
  46. OrthogonalLine(K_1, xAxis) → i
  47. OrthogonalLine(M_1, xAxis) → j
  48. OrthogonalLine(O_1, xAxis) → l
  49. OrthogonalLine(L_1, xAxis) → m
  50. OrthogonalLine(N_1, xAxis) → n
  51. OrthogonalLine(P_1, xAxis) → a_1
  52. Circle(I_1, 6.5) → f_1
  53. Intersect(f_1, d) → Q_1, R_1
  54. Intersect(r, d, (-3.774228689632889, 2.1243967656986413)) → S_1
  55. Intersect(r, i, (-9.407954274837792, 1.2885117717905816)) → T_1
  56. Intersect(r, j, (-15.041679860042695, 0.2875058379927696)) → U_1
  57. Intersect(r, l, (-20.6754054452476, 0.023599916315999357)) → V_1
  58. Intersect(r, m, (1.8594968955720141, 1.2885117717905816)) → W_1
  59. Intersect(r, n, (7.493222480776917, 0.2875058379927696)) → Z_1
  60. Intersect(r, a_1, (13.126948065981821, 0.023599916315999357)) → A_2
  61. Segment(M_1, U_1) → b_1
  62. Segment(N_1, Z_1) → j_1
  63. Segment(P_1, A_2) → k_1
  64. Segment(I_1, Q_1) → h_1
  65. Segment(O_1, V_1) → l_1
  66. Circle(J_1, 7.5) → p_1
  67. Intersect(p_1, b) → B_2, C_2
  68. Segment(J_1, B_2) → m_1
  69. OrthogonalLine(D_2, xAxis) → n_1
  70. OrthogonalLine(E_2, xAxis) → q_1
  71. OrthogonalLine(F_2, xAxis) → r_1
  72. Mirror(n_1, m_1) → s_1
  73. Mirror(q_1, m_1) → t_1
  74. Mirror(r_1, m_1) → a_2
  75. Intersect(q, s_1, (-7.75562250181825, 1.8221829408666963)) → G_2
  76. Intersect(s_1, xAxis) → H_2
  77. Intersect(t_1, xAxis) → I_2
  78. Intersect(q, t_1, (-11.739372745974084, 0.4065839714153232)) → J_2
  79. Intersect(a_2, xAxis) → K_2
  80. Intersect(q, a_2, (-15.72312299012992, 0.03337444473412614)) → L_2
  81. Intersect(q, n_1, (0.21187798649342193, 1.8221829408666963)) → M_2
  82. Intersect(q, q_1, (4.195628230649257, 0.4065839714153229)) → N_2
  83. Intersect(q, r_1, (8.179378474805093, 0.03337444473412608)) → O_2
  84. Segment(K_2, L_2) → b_2
  85. Segment(I_2, J_2) → c_2
  86. Segment(N_2, E_2) → d_2
  87. Segment(O_2, F_2) → e_2
  88. OrthogonalLine(L_1, top) → i_2
  89. Intersect(i_2, top) → P_2
  90. OrthogonalLine(K_1, top) → j_2
  91. Intersect(top, j_2) → Q_2
  92. Segment(K_1, Q_2) → g_1
  93. Segment(L_1, P_2) → i_1
  94. OrthogonalLine(H_2, top) → k_2
  95. OrthogonalLine(D_2, top) → l_2
  96. Intersect(k_2, top) → R_2
  97. Intersect(l_2, top) → S_2
  98. Segment(H_2, R_2) → f_2
  99. Segment(D_2, S_2) → g_2