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Scatter Plot Creation: Random Point Generation and Visualization

Scatter Plot Creation: Random Point Generation and Visualization
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2023-08-15 22:00
SequenceCoordinate GeometryProbability & StatisticsSlider AnimationGraphing
This GeoGebra example demonstrates how to create scatter plots and visualize randomly generated coordinate data points. Key mathematical concepts include coordinate planes, random number generation, point sequence operations, and statistical data visualization. Construction highlights: using Random commands to generate coordinate data, creating point objects via Sequence and Zip, organizing data with Flatten, sorting and deduplicating with Sort and Unique, drawing characteristic lines with Polygon and Segment, and adding interactive animations through Sliders. Suitable for secondary school statistics and probability teaching, introductory data analysis for college prep, and GeoGebra command learning practice.

GeoGebra Commands & Parameters

  1. Flatten(Sequence[Sequence[1, 3], n, 1, 33]) → randomProbs
  2. Element(randomProbs, Mod[countQuestion, 99] + 1) → randomProb
  3. PixelsToPoint(Corner[1], Corner[3], Corner[5], (11 + 5, 154)) → CornerLeftTable
  4. Shuffle(Sequence[Random[-100, 100] / 10, i, 1, 102]) → randomMult, {-2.3, -2.3, -4.8, 6.5, 5.9, 2.9, -7.7, -3.5, 5.7, 2.9, 2.2, -0.3, 7.7, 0.5, -1.7, -1.3, -9.9, -5.3, -5.2, -9.2, 7.3, 4.3, 0.7, 6.1, 4.5, -0.4, -9.7, 9.3, 2.8, 4.7, -9.3, -8.6, -8, -2.1, -1.5, 6.1, 4.6, 4, -2.2, -2.9, 9.5, 8.4, -1, 3.8, -4.2, -5.7, 6.9, -8.4, -7.9, 5.2, 2.3, -5.2, -6.9, -5, -2, 0.9, -3.8, -6.7, 8.5, 6.4, 0, -4.2, -5.7, 8, 2.5, 1.6, 5.9, -3.1, 3.1, 9.5, -4.5, -7.7, -0.7, 6, 4.9, -5.4, -3.7, 6.9, -0.6, 7.4, -3.3, -9, 5.5, -1, -0.6, -1.9, -0.3, 2.7, -7.1, -0.2, 8.5, 10, 9.4, -6.1, 1.8, 5, 4, 1.2, 9.1, -8.5, -6.9, -1.8}
  5. Shuffle(Sequence[Random[10, 20], i, 1, 102]) → randomRecip, {19, 13, 19, 13, 17, 10, 18, 18, 10, 17, 20, 15, 18, 11, 19, 17, 19, 14, 13, 19, 20, 14, 17, 15, 17, 18, 14, 12, 17, 14, 18, 15, 20, 12, 10, 15, 14, 20, 11, 14, 12, 15, 12, 14, 11, 13, 16, 13, 10, 17, 14, 18, 13, 16, 13, 19, 19, 12, 19, 20, 13, 17, 14, 12, 10, 17, 16, 14, 13, 13, 17, 13, 16, 15, 18, 18, 15, 10, 13, 12, 12, 11, 13, 11, 19, 19, 16, 11, 14, 17, 18, 20, 13, 16, 15, 15, 17, 14, 11, 18, 15, 17}
  6. Shuffle(Sequence[Random[0, 60] / 10, i, 1, 102]) → randomXH, {3.8, 1.2, 0.5, 4.5, 5.7, 0.4, 1.5, 6, 0.6, 3, 0.5, 4, 1.3, 2.8, 5.7, 2.3, 3.9, 3.1, 0.8, 5.3, 5.9, 0, 1, 1.2, 1.9, 0.8, 4.3, 3.3, 4.4, 5.3, 2.4, 2.3, 2.2, 0.7, 4.9, 1.2, 4.9, 0.6, 1.5, 0, 2.8, 4.4, 0.2, 5, 3.3, 2.9, 1.1, 0.8, 2.1, 5.3, 5.4, 2.1, 0.2, 2.2, 5.4, 3.5, 1.9, 2.2, 4.8, 5.3, 0.8, 0.6, 2, 0.3, 5.6, 0, 0.3, 0.9, 2.3, 3.3, 3.7, 5.9, 2.4, 4.2, 4.1, 4.3, 0.4, 1.1, 0.6, 2.3, 3.3, 5.4, 1, 1, 4.4, 2.2, 1.3, 0.7, 0.7, 1.5, 5.9, 4.9, 4.9, 4, 5, 4.1, 3.6, 0.5, 6, 0.1, 0.2, 4.4}
  7. Shuffle(Sequence[Random[100, 138] / 10, n, 1, 100]) → randomSlopes1, {12.5, 12.6, 12.9, 13.7, 10.2, 13.6, 11.2, 11.3, 12.5, 10.9, 12.7, 12.2, 12.2, 13.3, 11.7, 10.4, 13, 10.7, 10.3, 12.2, 12.5, 12.7, 13, 12.4, 12.4, 10, 11.5, 11.9, 10.7, 10.5, 10, 12.9, 12.5, 12.6, 12.1, 11.1, 13.1, 10.8, 12.7, 10.3, 10.4, 11.7, 13, 13.4, 13.2, 11.6, 13.6, 13.2, 11.2, 10.3, 10.4, 13.2, 11.7, 12.2, 10.2, 13.8, 12.8, 12, 13.3, 10, 13.3, 11.9, 11.3, 11.6, 12.3, 11.7, 11.8, 11.4, 11.8, 13.5, 12.7, 12.4, 10.7, 12.6, 13.1, 13, 11, 12.8, 10.6, 12, 12.8, 11.4, 12.9, 11, 11.6, 11.9, 12.2, 13.2, 13.5, 12.6, 13.7, 13.1, 12.4, 12.4, 12.7, 10.4, 11.7, 10.3, 11.8, 12.6}
  8. Element(randomSlopes1, Mod[countQuestion, 100] + 1) → randomSlope1
  9. Shuffle(Sequence[Random[-32, -20] / 10, n, 1, 100]) → randomSlopes2, {-2.9, -2.2, -2.7, -2.8, -2.8, -2.9, -2.7, -2.9, -3.2, -2.2, -2.7, -2.4, -2.8, -2, -3, -2.3, -2.8, -3.1, -2, -2.1, -2.9, -2.7, -2.2, -2.4, -2.7, -2.8, -2.5, -2.4, -2.4, -2.1, -2, -2.2, -2.9, -2.3, -2.9, -2.7, -2.9, -2.6, -2.9, -2.6, -2, -2.8, -2, -2.9, -3.1, -2.5, -2.8, -3, -2, -2.8, -3, -2.2, -3, -2, -2.4, -2.9, -2.4, -2.4, -2.2, -2.2, -2.5, -2, -2.6, -3.2, -2.3, -2.7, -2.2, -3.2, -3.1, -2.8, -3.1, -2, -2.3, -2.5, -2.9, -2, -2.7, -2.1, -2.4, -3, -2.2, -2, -2.4, -2.7, -2.2, -2.3, -2.1, -2.9, -2.4, -3.1, -2.4, -2.9, -2.3, -3.2, -2.4, -2.1, -3, -2.3, -2.6, -2.7}
  10. Element(randomSlopes2, Mod[countQuestion, 100] + 1) → randomSlope2
  11. Shuffle(Sequence[Random[1, 6], n, 1, 102]) → problem3x, {6, 5, 3, 5, 3, 4, 4, 2, 5, 2, 6, 1, 2, 1, 4, 1, 6, 4, 1, 5, 2, 5, 6, 5, 2, 4, 6, 6, 3, 3, 4, 3, 6, 5, 5, 5, 3, 6, 6, 5, 6, 4, 6, 5, 4, 1, 1, 2, 4, 2, 6, 1, 3, 4, 6, 1, 4, 4, 5, 4, 5, 3, 4, 4, 4, 1, 5, 3, 4, 5, 2, 2, 5, 2, 4, 3, 2, 2, 6, 5, 5, 5, 5, 2, 1, 1, 5, 5, 3, 6, 6, 2, 3, 1, 5, 6, 1, 4, 1, 1, 5, 5}
  12. Shuffle(Sequence[(round(Random[20, 100] / 5) * 5), n, 1, 102]) → problem3y, {60, 25, 40, 85, 70, 40, 45, 35, 65, 20, 20, 80, 75, 55, 85, 65, 60, 100, 25, 45, 85, 60, 95, 85, 65, 95, 45, 45, 60, 95, 40, 40, 65, 95, 55, 45, 90, 80, 20, 65, 65, 90, 75, 80, 100, 40, 80, 90, 50, 45, 65, 65, 100, 55, 70, 40, 50, 60, 35, 30, 40, 75, 35, 90, 30, 35, 25, 85, 25, 40, 65, 75, 40, 80, 40, 50, 30, 85, 25, 75, 100, 50, 90, 45, 55, 25, 35, 25, 70, 85, 35, 20, 30, 80, 35, 65, 95, 25, 25, 70, 40, 60}
  13. Unique(randomPoints3) → randomPoints3U
  14. Length(randomPoints3U) → lengthUnique3
  15. If(6 < Mod[(6 * (countQuestion + 1)), lengthUnique3] < lengthUnique3, Take[randomPoints3U, Mod[(6 * countQuestion), lengthUnique3] + 1, Mod[(6 * (countQuestion + 1)), lengthUnique3]], Mod[(6 * (countQuestion + 1)), lengthUnique3] ≟ 0, Last[randomPoints3U, 6], Join[{Last[randomPoints3U, 6 - Mod[(6 * (countQuestion + 1)), lengthUnique3]], First[randomPoints3U, Mod[(6 * (countQuestion + 1)), lengthUnique3]]}]) → uniqueRandomPoints3
  16. If(randomProb ≠ 2, ((42 + 2) * pixelHeightConvert), ((55 + 2) * pixelHeightConvert)) → titleHeight
  17. If(randomProb ≟ 2, 20, 100) → numMax
  18. If(randomProb ≟ 1, randomSlope1, randomProb ≟ 2, randomSlope2, 0) → randomSlope
  19. Zip((n, guideLine(n) + c / k), n, randomXH, c, randomMult, k, randomRecip) → problemPoints12
  20. Zip((round(x(n)), (round((y(n) * If[randomProb ≟ 2, 1, 0.2])) * If[randomProb ≟ 2, 1, 5])), n, problemPoints12) → problemPoints12Rounded
  21. Unique(KeepIf[y(n) < numMax, n, problemPoints12Rounded]) → problemPoints12U
  22. Length(problemPoints12U) → lengthUnique12
  23. If(6 < Mod[(6 * (countQuestion + 1)), lengthUnique12] < lengthUnique12, Take[problemPoints12U, Mod[(6 * countQuestion), lengthUnique12] + 1, Mod[(6 * (countQuestion + 1)), lengthUnique12]], Mod[(6 * (countQuestion + 1)), lengthUnique12] ≟ 0, Last[problemPoints12U, 6], Join[{Last[problemPoints12U, 6 - Mod[(6 * (countQuestion + 1)), lengthUnique12]], First[problemPoints12U, Mod[(6 * (countQuestion + 1)), lengthUnique12]]}]) → uniqueRandomPoints12
  24. If(randomProb ≟ 3, uniqueRandomPoints3, uniqueRandomPoints12) → randomPoints
  25. Sort(Zip[(round(x(n)), If[y(n) < 0, 0, y(n)]), n, randomPoints]) → randomPointsRounded
  26. If(randomProb ≟ 2, 0.2, 1) → scalingFactor
  27. Flatten(Sequence[Sequence[(n / 2, ((5 * m) * scalingFactor)), n, -6, 12], m, 0, 20]) → DragPoints
  28. Point(DragPoints) → InputPoint1
  29. Point(DragPoints) → InputPoint6
  30. Point(DragPoints) → InputPoint5
  31. Point(DragPoints) → InputPoint4
  32. Point(DragPoints) → InputPoint3
  33. Point(DragPoints) → InputPoint2
  34. Zip((x(n), y(n)), n, answerInput1) → answerInput
  35. KeepIf(¬(n ∈ answerInput), n, randomPointsRounded) → errorList
  36. Polygon({(-2.5, (105 * scalingFactor)), (-2.5, (-1 * scalingFactor)), (6.5, (-1 * scalingFactor)), (6.5, (105 * scalingFactor))}) → DragArea
  37. Sort(answerInput) → answerInputSorted
  38. Zip(n ∈ randomPointsRounded, n, answerInput) → boolCorrects
  39. Zip(abs(y(m) - y(n)), m, answerInputSorted, n, randomPointsRounded) → solutionYDifferences
  40. Zip(abs(x(m) - x(n)), m, answerInputSorted, n, randomPointsRounded) → solutionXDifferences
  41. Zip(n ≟ 0 ∧ m ≤ (2 * scalingFactor), n, solutionXDifferences, m, solutionYDifferences) → boolCorrectPoints
  42. Polygon(graphDimPoints) → graphArea
  43. Shuffle(Sequence[Random[20, 100], n, 1, 100]) → randomList2, {63, 23, 32, 22, 54, 56, 94, 40, 28, 86, 28, 36, 100, 30, 71, 21, 72, 47, 52, 75, 49, 65, 75, 35, 88, 74, 82, 32, 53, 38, 30, 98, 38, 100, 39, 72, 85, 95, 94, 73, 84, 23, 62, 34, 23, 30, 80, 68, 41, 92, 60, 71, 25, 92, 71, 61, 99, 79, 87, 98, 55, 64, 64, 33, 85, 96, 20, 63, 64, 79, 23, 61, 41, 96, 76, 24, 41, 60, 96, 41, 84, 52, 95, 57, 69, 87, 50, 34, 99, 44, 22, 30, 78, 62, 47, 86, 67, 20, 26, 66}
  44. Element(randomList2, Mod[countQuestion, 15] + 1) → randomNum2
  45. Shuffle(Sequence[Random[1, 6], n, 1, 100]) → randomList1, {5, 2, 5, 5, 5, 4, 6, 5, 6, 6, 3, 2, 5, 6, 5, 5, 3, 6, 5, 2, 5, 3, 6, 1, 5, 6, 4, 3, 2, 5, 2, 1, 2, 4, 3, 4, 2, 5, 3, 2, 3, 4, 4, 3, 4, 3, 2, 5, 1, 5, 5, 5, 3, 1, 3, 2, 2, 4, 2, 5, 1, 3, 3, 4, 3, 6, 2, 3, 1, 2, 1, 4, 5, 5, 2, 1, 6, 5, 1, 4, 5, 1, 2, 6, 2, 4, 4, 4, 2, 3, 2, 3, 2, 1, 2, 5, 3, 4, 2, 1}
  46. Element(randomList1, Mod[countQuestion, 20] + 1) → randomNum1
  47. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  48. Corner(5) → layoutAppSize
  49. Flatten(Sequence[6 / Random[20, 100], n, 1, 100]) → scatterLines
  50. Shuffle(Sequence[Random[20, 30], n, 1, 100]) → randomInts, {22, 23, 29, 27, 24, 26, 29, 23, 29, 22, 30, 22, 25, 23, 22, 21, 24, 23, 28, 25, 20, 22, 23, 20, 21, 24, 21, 25, 21, 20, 22, 26, 29, 20, 26, 20, 21, 25, 27, 25, 23, 22, 25, 30, 30, 28, 23, 22, 23, 24, 20, 23, 26, 29, 22, 22, 21, 29, 23, 29, 26, 22, 20, 25, 22, 20, 25, 28, 20, 26, 24, 22, 23, 23, 30, 27, 22, 21, 27, 22, 29, 30, 30, 27, 22, 30, 23, 26, 20, 21, 29, 20, 22, 20, 26, 21, 23, 20, 20, 23}
  51. Segment((0, 0), (graphDims(3), 0)) → axisX
  52. Segment((0, 0), (0, graphDims(4))) → axisY
  53. Shuffle(Sequence[Random[1, 2], n, 1, 100]) → randomOrders, {1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 2, 2, 1, 1, 1, 2, 2, 1, 2, 1, 2, 1, 1, 1, 2, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 2, 1, 2, 1, 2, 2, 2, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 2, 1, 2, 2, 2, 2, 1, 2}
  54. Element(randomOrders, Mod[countQuestion, 100] + 1) → randomOrder
  55. Distance(Corner[sizeLabelX, 1], Corner[sizeLabelX, 2]) → numLabelXW
  56. Distance(Corner[sizeLabelY, 1], Corner[sizeLabelY, 2]) → numLabelYW
  57. Join({{tableLabel(1) + "&" + (tableLabel(2)) + "\vphantom{\frac{a}{b}}\\\hline"}, Sequence["" + (x(randomPointsRounded(n))) + "&" + (y(randomPointsRounded(n))) + "\vphantom{\large{|}}\\\hline", n, 1, 6]}) → textListForTable
  58. Sum(textListForTable) → textForTable
  59. Polygon(Sequence[Corner[textLabelX, n], n, 1, 4]) → boxAxisXLabel
  60. Polygon(Sequence[Corner[textLabelY, n], n, 1, 4]) → boxAxisYLabel
  61. Polygon(polygonCoords) → dragArea
  62. Corner(sizingText, 4) → CornerSizing
  63. Sequence(Corner[textLabelX, n], n, 1, 4) → xLabelCorners
  64. Sequence(Corner[textLabelY, n], n, 1, 4) → yLabelCorners
  65. VerticalText(textLabelY) → vertLabelY
  66. VerticalText(textLabelY) → sizeLabelYVert
  67. Distance(Corner[sizeLabelYVert, 1], Corner[sizeLabelYVert, 4]) → numVertYH
  68. Translate(PolygonCoordsStart, Vector[(2 * Vector[CornerSizing, PolygonCoordsStart])]) → StartInputPoint
  69. RemoveUndefined(Sequence[If[boolCorrectPoints(n), answerInputSorted(n)], n, 1, 6]) → correctPoints
  70. makeBox(CornerLeftTable, rowWidth, boxHeight) → hintBox
  71. If(animationSlider < 0.3, 0, animationSlider - 0.3) → animationSlider1
  72. PartitionPoint(HintPoint1, HintPoint3, animationSlider1, 1) → HintAnimate1
  73. PartitionPoint(HintPoint2, HintPoint3, animationSlider1, 1) → HintAnimate2
  74. Segment(HintPoint2, HintAnimate2 - (0.15, 0)) → hintSeg2
  75. Segment(HintPoint1, HintAnimate1 - (0, (2.4 * scalingFactor))) → hintSeg1
  76. Translate(hintBox, Vector[(0, ((-numFirstIncorrect) * rowHeight) - titleHeight)]) → hintBoxFirst
  77. Translate(hintBox, Vector[(0, ((-numFirstIncorrect) * rowHeight) - titleHeight)]) → hintBoxOutline
  78. Remove(answerInput, randomPointsRounded) → errorListInput
  79. Intersection(answerInput, randomPointsRounded) → solutionList
  80. Zip(PartitionPoint[n, m, animationSlider2, 1], n, Sort[errorListInput], m, Sort[errorList]) → solutionAnimation
  81. Sum({tableLabel(1) + "&" + (tableLabel(2)) + "\vphantom{\frac{a}{b}}\\\hline"}) → textForTitle
  82. Sum({"" + (x(randomPointsRounded(1))) + "&" + (y(randomPointsRounded(1))) + "\vphantom{\large{|}}\\\hline"}) → textForRow
  83. expandCircle(InputPoint1, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI Drawing Prompt Reference

The graphic consists of a set of randomly generated scatter points whose coordinates are generated from random numbers, deduplicated and sorted. The points are distributed on a coordinate plane, with some marked as special points. A rectangular region is included to indicate the draggable data range, and a border frames the entire scatter area. The overall design is intended for statistics and probability teaching, illustrating random point distribution and data visualization.
The prompt above was compiled from the original drawing commands and is for reference only.