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Dice Roll Frequency Simulator with Bar Chart Statistics

Dice Roll Frequency Simulator with Bar Chart Statistics
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2020-08-07 18:01
FunctionSequenceProbability & StatisticsSlider AnimationGraphing
In collections !Statistics
This example demonstrates a dice-rolling simulation that repeatedly generates the occurrence frequencies of outcomes and visualizes the resulting distribution using a bar chart, highlighting how it stabilizes as the number of trials increases. Key mathematics includes probability, relative frequency (empirical probability), discrete distributions, and identifying the maximum frequency (the mode of the observed results) for comparison across outcomes. Construction uses GeoGebra commands such as Max and Sum to compute aggregated statistics and the peak frequency, and BarChart to render the frequency distribution. Objects like Throw50 and AntalTärningar represent the trial/sample size, while D1 through D34 store the frequency-related values for each outcome category. Additional text and helper objects (e.g., text1, Sidantal, LKum, MaxFrekvens) label the chart and present computed results. Suitable for middle and high school to introductory undergraduate probability & statistics lessons, classroom demonstrations, and exploratory modeling to build intuition about convergence of empirical frequencies to theoretical probabilities.

GeoGebra Commands & Parameters

  1. Max(RemoveUndefined[{Max[Frequency[LKum]], 0}]) → MaxFrekvens
  2. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D1
  3. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D2
  4. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D3
  5. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D4
  6. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D5
  7. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D6
  8. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D7
  9. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D8
  10. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D9
  11. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D10
  12. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D11
  13. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D12
  14. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D13
  15. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D14
  16. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D15
  17. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D16
  18. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D17
  19. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D18
  20. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D19
  21. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D20
  22. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D21
  23. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D22
  24. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D23
  25. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D24
  26. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D25
  27. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D26
  28. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D27
  29. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D28
  30. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D29
  31. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D30
  32. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D31
  33. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D32
  34. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D33
  35. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D34
  36. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D35
  37. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D36
  38. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D37
  39. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D38
  40. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D39
  41. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D40
  42. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D41
  43. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D42
  44. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D43
  45. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D44
  46. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D45
  47. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D46
  48. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D47
  49. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D48
  50. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D49
  51. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D50
  52. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D51
  53. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D52
  54. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D53
  55. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D54
  56. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D55
  57. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D56
  58. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D57
  59. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D58
  60. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D59
  61. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D60
  62. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D61
  63. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D62
  64. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D63
  65. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D64
  66. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D65
  67. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D66
  68. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D67
  69. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D68
  70. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D69
  71. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D70
  72. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D71
  73. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D72
  74. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D73
  75. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D74
  76. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D75
  77. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D76
  78. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D77
  79. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D78
  80. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D79
  81. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D80
  82. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D81
  83. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D82
  84. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D83
  85. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D84
  86. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D85
  87. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D86
  88. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D87
  89. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D88
  90. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D89
  91. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D90
  92. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D91
  93. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D92
  94. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D93
  95. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D94
  96. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D95
  97. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D96
  98. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D97
  99. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D98
  100. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D99
  101. Sum(Sequence[Random[1, Sidantal], a, 1, AntalTärningar]) → D100
  102. BarChart(LKum, 1) → a
  103. Max(RemoveUndefined[{a, 0}]) → b

AI Drawing Prompt Reference

Create a dice-rolling frequency simulator that visualizes empirical frequencies with a bar chart. Add a slider for the sample size and repeatedly run trials of a discrete dice-like experiment; for each outcome category, compute the observed count/frequency and store these values in a set of frequency statistics objects (covering the same 34 outcome slots used for the distribution). Determine the maximum frequency among the stored values as the peak for comparison. Render a bar chart whose bars correspond to the frequency at each outcome slot, and place text labels that report the current trial size and the maximum frequency (mode of the observed results), highlighting how the distribution stabilizes as trials increase.
The prompt above was compiled from the original drawing commands and is for reference only.