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Dragged Distribution

Dragged Distribution
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2014-09-17 01:58
Coordinate GeometryProbability & StatisticsOptimizationSlider AnimationGraphing
In collections Statistical Intuition Builders
This example demonstrates how moving discrete data points affects the distribution shape. Core math concepts include distribution, mean, standard deviation, and box plot. Construction involves commands like Polygon, PointIn, SD, Mean, Normal, BoxPlot, Segment, Intersect, Point, OrthogonalLine, Mirror, Integral, and objects S, R, Q, P_1, etc. Suitable for high school and above to understand dynamic changes in data distribution, ideal for probability & statistics education.

GeoGebra Commands & Parameters

  1. Polygon(P_1, Q, R, S) → poly1, p, q, r, s
  2. PointIn(poly1) → B
  3. PointIn(poly1) → C
  4. PointIn(poly1) → D
  5. PointIn(poly1) → E
  6. PointIn(poly1) → F
  7. PointIn(poly1) → G
  8. PointIn(poly1) → H
  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(poly1) → O
  16. PointIn(poly1) → A
  17. SD(X) → sd
  18. Mean(X) → mean
  19. Normal(mean, sd, x) → f
  20. BoxPlot(-0.02, 0.01, X, true) → median
  21. Segment(T, U) → a
  22. Intersect(a, xAxis) → V
  23. Point(xAxis) → P
  24. OrthogonalLine(P, xAxis) → b
  25. Point(Circle[V, abs(sd)]) → SD_1
  26. Segment(V, SD_1) → c
  27. Point(Circle[V, abs((2 * sd))]) → SD_2
  28. Segment(V, SD_2) → d
  29. Point(Circle[V, abs((3 * sd))]) → SD_3
  30. Segment(V, SD_3) → e
  31. OrthogonalLine(SD_1, xAxis) → g
  32. OrthogonalLine(SD_2, xAxis) → h
  33. OrthogonalLine(SD_3, xAxis) → i
  34. Mirror(SD_1, a) → SD_n1
  35. Mirror(SD_2, a) → SD_n2
  36. Mirror(SD_3, a) → SD_n3
  37. OrthogonalLine(SD_n3, xAxis) → j
  38. OrthogonalLine(SD_n2, xAxis) → k
  39. OrthogonalLine(SD_n1, xAxis) → l
  40. Integral(f, -Infinity, x(P)) → m
  41. Intersect(f, l, (8.196150479331507, 0.025765600325250028)) → Z
  42. Intersect(f, k, (-1.1950812973259275, 0.005749082526893479)) → A_1
  43. Intersect(f, j, (-10.58631307398337, 4.7191343130873153E-4)) → B_1
  44. Intersect(f, g, (26.97861403264639, 0.025765600325250028)) → C_1
  45. Intersect(f, h, (36.369845809303825, 0.005749082526893479)) → D_1
  46. Intersect(f, i, (45.76107758596127, 4.7191343130873153E-4)) → E_1
  47. Intersect(j, t) → F_1
  48. Intersect(k, t) → G_1
  49. Intersect(l, t) → H_1
  50. Intersect(g, t) → I_1
  51. Intersect(h, t) → J_1
  52. Intersect(i, t) → K_1
  53. Intersect(b, t) → L_1
  54. Intersect(f, b, (2.3743156048055805, 0.011438284314040505)) → M_1
  55. Segment(F_1, B_1) → a_1
  56. Segment(G_1, A_1) → b_1
  57. Segment(L_1, M_1) → c_1
  58. Segment(H_1, Z) → d_1
  59. Segment(I_1, C_1) → e_1
  60. Segment(J_1, D_1) → f_1
  61. Segment(K_1, E_1) → g_1

AI Drawing Prompt Reference

Draw a polygon with randomly generated points inside to show how moving these points affects data distribution. Calculate the mean and standard deviation of the points, plot a normal distribution curve to represent the data distribution, and create a box plot. Mark the mean and standard deviation on the coordinate axis, and draw corresponding standard deviation lines. Finally, complete the graphic display through integration and reflection operations.
The prompt above was compiled from the original drawing commands and is for reference only.