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Z分数与分位数

Z分数与分位数
几何画板及绘图内容加载中，请稍等……
2013-01-10 22:19
函数微积分概率统计函数图像
所属专题 Probability & Statistics
①本范例演示了Z分数与分位数在几何分布中的关系，通过可视化展示数据分布特征；②涉及核心数学概念包括Z分数计算、正态分布、分位数、几何分布特性；③构造要点：使用Function绘制函数，Intersect求交点，Point创建点，Vector生成向量，Segment画线段，Integral计算积分，Textfield添加文本，Line画直线，Translate平移，Max取最大值，InverseNormal生成正态分布逆函数；④适合高中及以上学生及数学爱好者学习概率统计与数据分析。

GeoGebra 命令及参数

  1. Function(exp((-(x)^(2)) / 2) / (sqrt(2 * π) * abs(1)), -3.4, 3.4) → f
  2. Function(0 * x - 0.0050, -3.7, 3.7) → a
  3. Intersect(a, b) → B
  4. Intersect(f, e, (-1, 0.24197072451914337)) → C
  5. Intersect(a, e) → D
  6. Intersect(f, d, (1, 0.24197072451914337)) → E
  7. Intersect(f, a, (-11.403406098005684, 2.309876005005087E-29)) → F
  8. Intersect(a, d) → G
  9. Intersect(f, j, (-2, 0.05399096651318806)) → H
  10. Intersect(f, a, (-11.40340609634047, 2.3098760488675827E-29)) → I
  11. Intersect(a, j) → J
  12. Intersect(f, i, (2, 0.05399096651318806)) → K
  13. Intersect(f, a, (-11.403406096916385, 2.3098760336977258E-29)) → L
  14. Intersect(a, i) → M
  15. Point(f) → N
  16. Point(f) → O
  17. Vector(O, N) → u
  18. Point(f) → P
  19. Point(f) → Q
  20. Vector(Q, P) → v
  21. Point(a) → R
  22. Point(a) → S
  23. Point(a) → T
  24. Point(a) → U
  25. Vector(S, T) → w
  26. Vector(R, U) → z
  27. Intersect(a, f, (-11.403406096339166, 0)) → W
  28. Intersect(a, f, (-11.403406096390832, 0)) → Z
  29. Segment(H, (-2, -0.06)) → k
  30. Segment(C, (-1, -0.06)) → g
  31. Segment(A, (0, -0.06)) → c
  32. Segment(E, (1, -0.06)) → h
  33. Segment(K, (2, -0.06)) → l
  34. Integral(f, -3.6, zscore) → AreaUnder
  35. Textfield(zscore) → inputBox1
  36. Function(f(x) - 0.0030, -3.5, zscore) → AreaCurve
  37. Integral(a(x) + 0.0050, -3.6, zscore) → AddABitUnder
  38. Function(a(x) + 0.0025, -3.5, zscore) → Areax
  39. Segment((zscore, -0.02), (zscore, AreaCurve(zscore))) → AreaRight
  40. Textfield(XDistStandardDeviation) → inputσ
  41. Textfield(XDistMean) → inputμ
  42. Line(D_1, xAxis) → m
  43. Point(m) → E_1
  44. Vector(D_1, E_1) → n
  45. Function(exp((-(x - ndist)^(2)) / 2) / (sqrt(2 * π) * abs(1)), -3.4 + ndist, 3.4 + ndist) → fTrans
  46. Vector((x(Q) + ndist, y(Q)), (x(P) + ndist, y(P))) → v'
  47. Translate(h, n) → h'
  48. Translate(l, n) → l'
  49. Segment((3, 0), (3, -0.06)) → ThreeSigRight
  50. Translate(ThreeSigRight, n) → ThreeSigRight'
  51. Translate(c, n) → c'
  52. Translate(g, n) → g'
  53. Segment((-3, 0), (-3, -0.06)) → ThreeLeft
  54. Translate(ThreeLeft, n) → ThreeLeft'
  55. Translate(k, n) → k'
  56. Max(f, -2, 2) → MaxZDist
  57. Translate(U, n) → U'
  58. Translate(R, n) → R'
  59. Translate(S, n) → S'
  60. Translate(T, n) → T'
  61. Segment(S', R') → p
  62. Vector(R', U') → q
  63. Vector(S', T') → r
  64. Translate(AreaRight, n) → AreaRight'
  65. Integral(fTrans, -3.6 + ndist, zscore + ndist) → TAreaUnder
  66. Function(a(x + ndist) + 0.0025, -3.5 + ndist, zscore + ndist) → TArea
  67. Max(exp((-((x - XDistMean) / XDistStandardDeviation)^(2)) / 2) / (sqrt(2 * π) * abs(XDistStandardDeviation)), XDistMean - 1, XDistMean + 1) → FindNewMax
  68. Translate(MaxZDist, n) → MaxZDist'
  69. Vector((x(O) + ndist, y(O)), (x(N) + ndist, y(N))) → u'
  70. Translate(ZScorePt, n) → ZScorePt'
  71. Translate(PtToTranslate, n) → PtToTranslate'
  72. Vector(ZScorePt', PtToTranslate') → s
  73. InverseNormal(0, 1, AreaUnder) → InvNorm
  74. Integral(f, zscore, 3.5) → RightAreaUnder
  75. Integral(fTrans, zscore + ndist, 3.6 + ndist) → RightAreaXDist
  76. Vector((zscore, -0.175), (zscore, -0.04)) → ShowZscoreQuantile

AI 绘图提示语参考

画一个正态分布曲线，并在其下方画一条水平线，标出两条线的交点。在正态分布曲线上标出几个点，并连接这些点与水平线上的对应点，形成几个小矩形。计算并显示这些矩形的面积，以及正态分布曲线与水平线之间的面积。同时，展示标准正态分布的图像，并标出均值和标准差。
以上提示语为根据原始绘图命令整理而来，仅供参考。