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Two Distributions - Mode, Median, Expected Value

Two Distributions - Mode, Median, Expected Value
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2020-05-28 19:08
FunctionCoordinate GeometryCalculusProbability & Statistics
This example demonstrates the calculation and visualization of mode, median, and expected value for two different distributions. Key math concepts include probability & statistics on distributions, mode, median, expected value, and coordinate geometry for data representation. Construction highlights GeoGebra commands like Segment, Point, mean, Median, If, Length, Sequence, and BarChart. Suitable for high school and above students learning probability statistics and data analysis.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw two distribution curves representing two different distributions. Mark the mode, median, and expected value on the x-axis for each distribution. The mode is where the peak of the curve is, the median is a vertical line that splits the curve in half, and the expected value is the center of the area under the curve.
The prompt above was compiled from the original drawing commands and is for reference only.