两个分布的众数、中位数与期望值

两个分布的众数、中位数与期望值
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2020-05-28 19:08
①本范例演示了两个不同分布的众数、中位数和期望值的计算与可视化;②涉及的核心数学概念包括概率统计中的分布、众数、中位数、期望值,以及解析几何中的数据表示;③作图要点提炼自GeoGebra命令:Segment(线段)、Point(点)、mean(均值)、Median(中位数)、If(条件判断)、Length(长度)、Sequence(数列)、BarChart(条形图);④适合高中及以上学生学习和理解概率统计与数据分析。

GeoGebra 命令及参数

  1. Segment((1, 0), (11, 0)) → thexaxis
  2. Point(thexaxis) → A12
  3. Point(thexaxis) → A13
  4. Point(thexaxis) → A14
  5. Point(thexaxis) → A15
  6. Point(thexaxis) → A16
  7. Point(thexaxis) → A17
  8. Point(thexaxis) → A18
  9. Point(thexaxis) → A19
  10. Point(thexaxis) → A20
  11. Point(thexaxis) → A21
  12. Point(thexaxis) → A22
  13. Point(thexaxis) → A23
  14. Point(thexaxis) → A24
  15. Point(thexaxis) → A25
  16. Point(thexaxis) → A26
  17. Point(thexaxis) → A27
  18. Point(thexaxis) → A28
  19. Point(thexaxis) → A29
  20. Point(thexaxis) → A30
  21. Point(thexaxis) → A31
  22. Point(thexaxis) → A32
  23. Point(thexaxis) → A33
  24. Point(thexaxis) → A34
  25. Point(thexaxis) → A35
  26. Point(thexaxis) → A36
  27. Point(thexaxis) → A37
  28. Point(thexaxis) → A38
  29. Point(thexaxis) → A39
  30. Point(thexaxis) → A40
  31. Point(thexaxis) → A41
  32. Point(thexaxis) → A42
  33. Point(thexaxis) → A43
  34. Point(thexaxis) → A44
  35. Point(thexaxis) → A45
  36. Point(thexaxis) → A46
  37. Point(thexaxis) → A47
  38. Point(thexaxis) → A48
  39. Point(thexaxis) → A49
  40. Point(thexaxis) → A50
  41. Point(thexaxis) → B13
  42. Point(thexaxis) → B14
  43. Point(thexaxis) → B15
  44. Point(thexaxis) → B16
  45. Point(thexaxis) → B17
  46. Point(thexaxis) → B18
  47. Point(thexaxis) → B19
  48. Point(thexaxis) → B20
  49. Point(thexaxis) → B21
  50. Point(thexaxis) → B22
  51. Point(thexaxis) → B23
  52. Point(thexaxis) → B24
  53. Point(thexaxis) → B25
  54. Point(thexaxis) → B26
  55. Point(thexaxis) → B27
  56. Point(thexaxis) → B28
  57. Point(thexaxis) → B29
  58. Point(thexaxis) → B30
  59. Point(thexaxis) → B31
  60. Point(thexaxis) → B32
  61. Point(thexaxis) → B33
  62. Point(thexaxis) → B34
  63. Point(thexaxis) → B35
  64. Point(thexaxis) → B36
  65. Point(thexaxis) → B37
  66. Point(thexaxis) → B38
  67. Point(thexaxis) → B39
  68. Point(thexaxis) → B40
  69. Point(thexaxis) → B41
  70. Point(thexaxis) → B42
  71. Point(thexaxis) → B43
  72. Point(thexaxis) → B44
  73. Point(thexaxis) → B45
  74. Point(thexaxis) → B46
  75. Point(thexaxis) → B47
  76. Point(thexaxis) → B48
  77. Point(thexaxis) → B49
  78. Point(thexaxis) → B50
  79. mean(thexs1) → mean1
  80. mean(thexs2) → mean2
  81. Median(thexs1) → median1
  82. Median(thexs2) → median2
  83. If(Length[Mode[thexs1]] ≟ 0, Sequence[10], Mode[thexs1]) → mode1
  84. If(Length[Mode[thexs2]] ≟ 0, Sequence[10], Mode[thexs2]) → mode2
  85. Length(mode1) → nummode1
  86. Length(mode2) → nummode2
  87. Segment((median1, (mediandepth * ymin)), (median1, 0)) → meadianpos1
  88. Segment((mean1, (meandepth * ymin)), (mean1, 0)) → meanpos1
  89. Segment((median2, (mediandepth * ymin)), (median2, 0)) → medianpos2
  90. Segment((mean2, (meandepth * ymin)), (mean2, 0)) → meanpos2
  91. Sequence(Segment[(mode1(i), ((1 / 2 * modedepth) * ymin)), (mode1(i), 0)], i, 1, nummode1) → modepos1
  92. Sequence(Segment[(mode2(i), ((1 / 2 * modedepth) * ymin)), (mode2(i), 0)], i, 1, nummode2) → modepos2
  93. Segment((Min[mode1], ((1 / 2 * modedepth) * ymin)), (Max[mode1], ((1 / 2 * modedepth) * ymin))) → modebar1
  94. Segment((Min[mode2], ((1 / 2 * modedepth) * ymin)), (Max[mode2], ((1 / 2 * modedepth) * ymin))) → modebar2
  95. Segment(((Min[mode1] + Max[mode1]) / 2, (modedepth * ymin)), ((Min[mode1] + Max[mode1]) / 2, ((1 / 2 * modedepth) * ymin))) → modelabel1
  96. Segment(((Min[mode2] + Max[mode2]) / 2, (modedepth * ymin)), ((Min[mode2] + Max[mode2]) / 2, ((1 / 2 * modedepth) * ymin))) → modelabel2
  97. Point(thexaxis) → B12
  98. BarChart(Sequence[11], freq1, 0.8) → dist1
  99. BarChart(Sequence[11], freq2, 0.8) → dist2
  100. Point(thexaxis) → A11
  101. Point(thexaxis) → B11
  102. Point(thexaxis) → A1
  103. Point(thexaxis) → A2
  104. Point(thexaxis) → A3
  105. Point(thexaxis) → A4
  106. Point(thexaxis) → A5
  107. Point(thexaxis) → A6
  108. Point(thexaxis) → A7
  109. Point(thexaxis) → A8
  110. Point(thexaxis) → A9
  111. Point(thexaxis) → A10
  112. Point(thexaxis) → B1
  113. Point(thexaxis) → B2
  114. Point(thexaxis) → B3
  115. Point(thexaxis) → B4
  116. Point(thexaxis) → B5
  117. Point(thexaxis) → B6
  118. Point(thexaxis) → B7
  119. Point(thexaxis) → B8
  120. Point(thexaxis) → B9
  121. Point(thexaxis) → B10

AI 绘图提示语参考

画两条分布曲线,分别表示两个不同的分布。在x轴上标出两个分布的模式、中位数和期望值。模式是曲线峰值对应的位置,中位数是将曲线分成两半的垂直线,期望值是曲线下的面积中心。
以上提示语为根据原始绘图命令整理而来,仅供参考。