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Standard Deviation & Variance

Standard Deviation & Variance
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2019-03-21 20:04
Coordinate GeometryProbability & StatisticsMatrixGeometric ConstructionGraphing
This example dynamically demonstrates the relationship between standard deviation, variance, and the shape of an ellipse, revealing the dispersion of data. Key math concepts include standard deviation, variance, ellipse, matrices, symmetry, general quadrilateral, and bar chart. GeoGebra commands and objects used in construction are mean (average), OrthogonalLine (perpendicular line), Intersect (intersection), Segment (segment), stdevp (population standard deviation), Median (median), Point (point), Name (naming), and TableText (table text). Suitable for high school and above learners to understand the intersection of statistics and analytical geometry.

GeoGebra Commands & Parameters

  1. mean(B1:B12) → B13
  2. OrthogonalLine(A, f) → g
  3. OrthogonalLine(B, f) → h
  4. OrthogonalLine(C, f) → i
  5. OrthogonalLine(D, f) → j
  6. OrthogonalLine(E, f) → k
  7. OrthogonalLine(F, f) → l
  8. OrthogonalLine(G, f) → m
  9. OrthogonalLine(H, f) → n
  10. OrthogonalLine(I, f) → p
  11. OrthogonalLine(J, f) → q
  12. OrthogonalLine(K, f) → r
  13. OrthogonalLine(L, f) → s
  14. Intersect(f, g) → M
  15. Intersect(f, h) → N
  16. Intersect(f, i) → O
  17. Intersect(f, j) → P
  18. Intersect(f, k) → Q
  19. Intersect(f, l) → R
  20. Intersect(f, m) → S
  21. Intersect(f, n) → T
  22. Intersect(f, p) → U
  23. Intersect(f, q) → V
  24. Intersect(f, r) → W
  25. Segment(A, M) → t
  26. Segment(B, N) → a
  27. Segment(C, O) → b
  28. Segment(D, P) → c
  29. Segment(E, Q) → d
  30. Segment(F, R) → e
  31. Segment(S, G) → f_1
  32. Segment(T, H) → g_1
  33. Segment(I, U) → h_1
  34. Segment(V, J) → i_1
  35. Segment(W, K) → j_1
  36. Intersect(f, s) → Z
  37. Segment(L, Z) → k_1
  38. stdevp(list2) → B15
  39. Median(B1:B12) → B14
  40. Intersect(f, yAxis) → A_1
  41. Point(f) → B_1
  42. Segment(A_1, B_1) → l_1
  43. Name(Standard) → C1
  44. TableText({{A13, B13}, {A14, B14}, {A15, B15}, {A16, B16}}, "|_") → text6