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Exploring Mean and Standard Deviation

Exploring Mean and Standard Deviation
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2018-04-19 07:43
FunctionProbability & Statistics
This example dynamically illustrates the concepts of mean and standard deviation. It involves core statistical concepts and allows users to observe changes in mean and standard deviation by adjusting data points. Commands used include Point, If, RemoveUndefined, Mean, Sum, Vector, Polygon, Circle, etc., suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(g) → B
  2. If(x(B) ≥ 0, x(B)) → b
  3. Point(k) → F
  4. If(x(F) ≥ 0, x(F)) → f
  5. Point(j) → E
  6. If(x(E) ≥ 0, x(E)) → e
  7. Point(i) → D
  8. If(x(D) ≥ 0, x(D)) → d
  9. Point(h) → C
  10. If(x(C) ≥ 0, x(C)) → c
  11. Point(l) → A
  12. If(x(A) ≥ 0, x(A)) → a
  13. RemoveUndefined(L_2) → L_1
  14. Mean(L_1) → m
  15. If(A1 - m < 0, 1, 0) → B1
  16. Mean({a, b, c, d, e, f}) → v
  17. If(A1 - m > 0, 1, 0) → C1
  18. If(A2 - m < 0, 1, 0) → B2
  19. If(A3 - m < 0, 1, 0) → B3
  20. If(A4 - m < 0, 1, 0) → B4
  21. If(A5 - m < 0, 1, 0) → B5
  22. If(A6 - m < 0, 1, 0) → B6
  23. If(A2 - m > 0, 1, 0) → C2
  24. If(A3 - m > 0, 1, 0) → C3
  25. If(A4 - m > 0, 1, 0) → C4
  26. If(A5 - m > 0, 1, 0) → C5
  27. If(A6 - m > 0, 1, 0) → C6
  28. Sum(D1:D6) → D7
  29. Sum(E1:E6) → E7
  30. Vector((m, 0), (m - D9, 0)) → D16
  31. Vector((m, 0), (m - D10, 0)) → D17
  32. Vector((m, 0), (m - D11, 0)) → D18
  33. Vector((m, 0), (m - D12, 0)) → D19
  34. Vector((m, 0), (m - D13, 0)) → D20
  35. Vector((m, 0), (m - D14, 0)) → D21
  36. Vector((m, 0), (m + E9, 0)) → E16
  37. Vector((m, 0), (m + E10, 0)) → E17
  38. Vector((m, 0), (m + E11, 0)) → E18
  39. Vector((m, 0), (m + E12, 0)) → E19
  40. Vector((m, 0), (m + E13, 0)) → E20
  41. Vector((m, 0), (m + E14, 0)) → E21
  42. Vector((m, (5 * sc)), (x(E), (5 * sc))) → n
  43. Vector((m, (4 * sc)), (x(D), (4 * sc))) → p
  44. Vector((m, (3 * sc)), (x(C), (3 * sc))) → q
  45. Vector((m, (2 * sc)), (x(B), (2 * sc))) → r
  46. Vector((m, sc), (x(A), sc)) → s
  47. Vector((m, (6 * sc)), (x(F), (6 * sc))) → w
  48. Polygon(C15, C16, (x(C16), (-D1)), (x(C15), (-D1))) → B16, t, f_1, g_1, h_1
  49. Vector((m, 0), (m, (7 * sc))) → u
  50. Polygon(C16, C17, (x(C17), (-D2)), (x(C16), (-D2))) → B17, i_1, j_1, k_1, l_1
  51. Polygon(C17, C18, (x(C18), (-D3)), (x(C17), (-D3))) → B18, m_1, n_1, p_1, q_1
  52. Polygon(C18, C19, (x(C19), (-D4)), (x(C18), (-D4))) → B19, r_1, s_1, t_1, a_1
  53. Polygon(C19, C20, (x(C20), (-D5)), (x(C19), (-D5))) → B20, b_1, c_1, d_1, e_1
  54. Polygon(C20, C21, (x(C21), (-D6)), (x(C20), (-D6))) → B21, f_2, g_2, h_2, i_2
  55. Polygon(F15, F16, (x(F16), (-E1)), (x(F15), (-E1))) → G16, H16_1, I16, J16, K16
  56. Polygon(F16, F17, (x(F17), (-E2)), (x(F16), (-E2))) → G17, H17_1, I17, J17, K17
  57. Polygon(F17, F18, (x(F18), (-E3)), (x(F17), (-E3))) → G18, H18_1, I18, J18, K18
  58. Polygon(F18, F19, (x(F19), (-E4)), (x(F18), (-E4))) → G19, H19_1, I19, J19, K19
  59. Polygon(F19, F20, (x(F20), (-E5)), (x(F19), (-E5))) → G20, H20_1, I20, J20, K20
  60. Polygon(F20, F21, (x(F21), (-E6)), (x(F20), (-E6))) → G21, H21_1, I21, J21, K21
  61. Circle((m, 0), D7) → c_2