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Dice Average

Dice Average
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2022-08-08 17:03
Coordinate GeometryProbability & Statistics
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This example demonstrates calculating the average of dice rolls. Key mathematical concepts include arithmetic mean, median, and mode. GeoGebra commands such as Shuffle and Sum are used for data processing and graphical representation. Suitable for 5th to 6th grade students to practice probability and statistics.

GeoGebra Commands & Parameters

  1. Shuffle(Sequence[Random[2, 5], i, 1, 100]) → gewAugenzahl, {3, 5, 3, 5, 3, 3, 4, 5, 5, 5, 4, 4, 5, 4, 2, 4, 4, 5, 5, 4, 5, 5, 5, 4, 5, 3, 3, 5, 3, 2, 5, 4, 3, 2, 3, 3, 4, 4, 5, 5, 5, 2, 2, 2, 5, 5, 2, 3, 5, 4, 2, 2, 4, 5, 2, 5, 4, 5, 4, 3, 4, 2, 2, 4, 3, 3, 4, 3, 5, 3, 3, 3, 4, 5, 3, 4, 4, 5, 4, 5, 5, 4, 2, 3, 3, 2, 4, 4, 3, 5, 5, 5, 3, 4, 3, 3, 2, 5, 5, 3}
  2. Append(true, Sequence[If[gewAugenzahl(i) ≟ gewAugenzahl(i - 1), false, true], i, 2, 100]) → stayX
  3. Remove(Sequence[If[stayX(i), gewAugenzahl(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForXwithoutRepeat
  4. Midpoint(Corner[B63, 1], Corner[B63, 3]) → MidPoint_{B63}
  5. Midpoint(Corner[B62, 1], Corner[B62, 3]) → MidPoint_{B62}
  6. Midpoint(Corner[B53, 1], Corner[B53, 3]) → MidPoint_{B53}
  7. Midpoint(Corner[B52, 1], Corner[B52, 3]) → MidPoint_{B52}
  8. Midpoint(Corner[B43, 1], Corner[B43, 3]) → MidPoint_{B43}
  9. Midpoint(Corner[B42, 1], Corner[B42, 3]) → MidPoint_{B42}
  10. Midpoint(Corner[B33, 1], Corner[B33, 3]) → MidPoint_{B33}
  11. Midpoint(Corner[B32, 1], Corner[B32, 3]) → MidPoint_{B32}
  12. Midpoint(Corner[B23, 1], Corner[B23, 3]) → MidPoint_{B23}
  13. Midpoint(Corner[B22, 1], Corner[B22, 3]) → MidPoint_{B22}
  14. Midpoint(Corner[B13, 1], Corner[B13, 3]) → MidPoint_{B13}
  15. Midpoint(Corner[B12, 1], Corner[B12, 3]) → MidPoint_{B12}
  16. Polygon(M, N, O, P) → v1, m, n, o, p
  17. IsInRegion(MidPoint_{B63}, v1) → in6_3
  18. IsInRegion(MidPoint_{B62}, v1) → in6_2
  19. IsInRegion(MidPoint_{B53}, v1) → in5_3
  20. IsInRegion(MidPoint_{B52}, v1) → in5_2
  21. IsInRegion(MidPoint_{B43}, v1) → in4_3
  22. IsInRegion(MidPoint_{B42}, v1) → in4_2
  23. IsInRegion(MidPoint_{B33}, v1) → in3_3
  24. IsInRegion(MidPoint_{B32}, v1) → in3_2
  25. IsInRegion(MidPoint_{B23}, v1) → in2_3
  26. IsInRegion(MidPoint_{B22}, v1) → in2_2
  27. IsInRegion(MidPoint_{B13}, v1) → in1_3
  28. IsInRegion(MidPoint_{B12}, v1) → in1_2
  29. Midpoint(Corner[Bild6, 1], Corner[Bild6, 3]) → MidPoint_{Bild6}
  30. IsInRegion(MidPoint_{Bild6}, v1) → in6
  31. Midpoint(Corner[Bild5, 1], Corner[Bild5, 3]) → MidPoint_{Bild5}
  32. IsInRegion(MidPoint_{Bild5}, v1) → in5
  33. Midpoint(Corner[Bild4, 1], Corner[Bild4, 3]) → MidPoint_{Bild4}
  34. IsInRegion(MidPoint_{Bild4}, v1) → in4
  35. Midpoint(Corner[Bild3, 1], Corner[Bild3, 3]) → MidPoint_{Bild3}
  36. IsInRegion(MidPoint_{Bild3}, v1) → in3
  37. Midpoint(Corner[Bild2, 1], Corner[Bild2, 3]) → MidPoint_{Bild2}
  38. IsInRegion(MidPoint_{Bild2}, v1) → in2
  39. Midpoint(Corner[Bild1, 1], Corner[Bild1, 3]) → MidPoint_{Bild1}
  40. IsInRegion(MidPoint_{Bild1}, v1) → in1
  41. Shuffle(Sequence[Random[3, 6], i, 1, 100]) → anzahlWürfelZiehbar, {3, 4, 3, 3, 4, 4, 4, 5, 3, 5, 4, 4, 3, 3, 4, 4, 6, 6, 5, 3, 5, 6, 5, 4, 4, 5, 5, 5, 6, 4, 6, 6, 3, 4, 4, 6, 6, 5, 3, 6, 3, 6, 4, 3, 5, 6, 3, 5, 4, 4, 3, 5, 5, 3, 5, 3, 4, 6, 4, 4, 4, 4, 5, 4, 3, 5, 3, 5, 4, 6, 4, 6, 6, 5, 3, 4, 6, 3, 3, 5, 6, 4, 4, 4, 4, 6, 3, 6, 3, 5, 3, 4, 5, 3, 6, 3, 4, 4, 6, 6}
  42. Element(anzahlWürfelZiehbar, Mod[questionCount, 100] + 1) → würfelZahl
  43. Element(randomNosForXwithoutRepeat, Mod[questionCount, 100] + 1) → augenZahl
  44. If(in1, 1, 0) → zahl1
  45. If(in2, 2, 0) → zahl2
  46. If(in3, 3, 0) → zahl3
  47. If(in4, 4, 0) → zahl4
  48. If(in5, 5, 0) → zahl5
  49. Sum(listeElementeInVieleck) → sumCorrect
  50. If(in6, 6, 0) → zahl6
  51. If(in1_2, 1, 0) → zahl1_2
  52. If(in1_3, 1, 0) → zahl1_3
  53. If(in2_2, 2, 0) → zahl2_2
  54. If(in2_3, 2, 0) → zahl2_3
  55. If(in3_2, 3, 0) → zahl3_2
  56. If(in3_3, 3, 0) → zahl3_3
  57. If(in4_2, 4, 0) → zahl4_2
  58. If(in4_3, 4, 0) → zahl4_3
  59. If(in5_2, 5, 0) → zahl5_2
  60. If(in5_3, 5, 0) → zahl5_3
  61. If(in6_2, 6, 0) → zahl6_2
  62. If(in6_3, 6, 0) → zahl6_3
  63. Sum(listeSumme) → augenSumme
  64. Textfield(aInput) → InputBox1
  65. Textfield(bInput) → InputBox2
  66. Polygon(PtopLeftCornerFeedback, PtopRightCornerFeedback, PbottomRightCornerFeedback, PbottomLeftCornerFeedback) → rectangleCorrect, ptopleftcornerfeedback, ptoprightcornerfeedback, pbottomrightcornerfeedback, pbottomleftcornerfeedback
  67. Append(true, Sequence[If[anzahlWürfelZiehbar(i) ≟ anzahlWürfelZiehbar(i - 1), false, true], i, 2, 100]) → stayY
  68. Remove(Sequence[If[stayY(i), anzahlWürfelZiehbar(i), 0], i, 1, 100], Sequence[0, i, 1, 100]) → randomNosForYwithoutRepeat
  69. Element(randomNosForXwithoutRepeat, Mod[questionCount, Length[randomNosForXwithoutRepeat]] + 1) → numXwithoutRepeat
  70. Element(randomNosForYwithoutRepeat, Mod[questionCount, Length[randomNosForYwithoutRepeat]] + 1) → numYwithoutRepeat
  71. Defined((aInput * bInput)) → fixed
  72. Polygon(Q, R, S, T) → v2, q, r, s, t
  73. Segment(U, V) → g
  74. Midpoint(Corner[Zweier, 1], Corner[Zweier, 3]) → MidPoint_{Bild8}
  75. Midpoint(Corner[Dreier, 1], Corner[Dreier, 3]) → MidPoint_{Bild9}
  76. Midpoint(Corner[Vierer, 1], Corner[Vierer, 3]) → MidPoint_{Bild10}
  77. Midpoint(Corner[Fünfer, 1], Corner[Fünfer, 3]) → MidPoint_{Bild11}
  78. If(in1, Append[zahl1, {}]) → anfügenArithm1
  79. If(in2, Append[zahl2, anfügenArithm1]) → anfügenArithm2
  80. If(in3, Append[zahl3, anfügenArithm2]) → anfügenArithm3
  81. If(in4, Append[zahl4, anfügenArithm3]) → anfügenArithm4
  82. If(in5, Append[zahl5, anfügenArithm4]) → anfügenArithm5
  83. If(in6, Append[zahl6, anfügenArithm5]) → anfügenArithm6
  84. Midpoint(Corner[Zweier, 1], Corner[Zweier, 3]) → MidPoint_{Zweier}
  85. Midpoint(Corner[Dreier, 1], Corner[Dreier, 3]) → MidPoint_{Dreier}
  86. Midpoint(Corner[Vierer, 1], Corner[Vierer, 3]) → MidPoint_{Vierer}
  87. Midpoint(Corner[Fünfer, 1], Corner[Fünfer, 3]) → MidPoint_{Fünfer}
  88. CountIf(x > 0, listeElementeInVieleck) → zähleWennTest
  89. Sum(gezogen) → sumIn

AI Drawing Prompt Reference

Create a visualization showing the average of dice rolls, including a sequence of 100 random dice numbers and a sequence with unique values obtained by removing duplicates. Connect the unique values to form a polygon. Then, represent the frequency of each number with different colored regions, highlighting the probability distribution.
The prompt above was compiled from the original drawing commands and is for reference only.