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Creating Scatter Plots

Creating Scatter Plots
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2023-01-27 12:51
Coordinate GeometryProbability & StatisticsGraphing
This example demonstrates how to create scatter plots by identifying axes and plotting points. The core math concepts involved are statistics, including organizing, displaying, and interpreting data, as well as determining positive, negative, or no correlation through scatter plots. Key GeoGebra commands used include RandomUniform, Take, PixelsToPoint, Zip, Unique, Length, If, Sort, Flatten, Point, KeepIf, Polygon, Corner, Segment, Distance, Join, Sum, Sequence, VerticalText, Translate, RemoveUndefined, makeBox, PartitionPoint, Remove, Intersection, expandCircle; objects like allRandoms, numRandoms, countQuestion, randIndex, currentRandomSeeds, randomProb, dimensionsAll, dimensions, pixelHeightConvert, boxHeight, pixelWidthConvert, rowWidth, CornerLeftTable, randomMult, randomRecip, randomXH, randomSlope1, randomSlope2, problem3x, problem3y, randomPoints3, randomPoints3U, lengthUnique3, uniqueRandomPoints3, titleHeight, rowHeight, numMax, randomSlope, guideLine, problemPoints12, problemPoints12Rounded, problemPoints12U, lengthUnique12, uniqueRandomPoints12, randomPoints, randomPointsRounded, scalingFactor, DragPoints, InputPoint1, InputPoint6. Suitable for students in grades 6-8 learning data analysis.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 400) → allRandoms, {0.4364967330707387, 0.8279794215391527, 0.4290004671891307, 0.06717012330957603, 0.8605279110658038, 0.3970423519998629, 0.7571751439757286, 0.3402434657518975, 0.5503796826218706, 0.22096660340787075, 0.4257581327249671, 0.3625300130213526, 0.6827924728731817, 0.40847179172775583, 0.3682300626589904, 0.19951292232032217, 0.47876048244123615, 0.8653074219773348, 0.266844854026304, 0.8059439764226863, 0.4444092525206932, 0.17363905755533662, 0.12234263903809962, 0.2916382486048643, 0.3997060167471245, 0.6759072554351157, 0.7735712797312612, 0.3233571984564109, 0.012247582505562382, 0.15993252142081008, 0.09806461414824516, 0.1364428196238672, 0.768086812559315, 0.7623036511773474, 0.32731125196725924, 0.29684855186737946, 0.2997136410545501, 0.128287304338225, 0.5015708368754435, 0.3871322861105321, 0.37289792029101787, 0.938636003778352, 0.01865525456168939, 0.7088340978597069, 0.799130849375167, 0.4867473342307885, 0.359090041427768, 0.9784565774944668, 0.2988686633985176, 0.05364147119569441, 0.0065073168835029106, 0.12499797411674321, 0.6226863228120381, 0.45317442586803086, 0.6469939003593178, 0.0836578181418435, 0.1527909338125303, 0.5257942473870935, 0.7344296563417425, 0.9429430363807179, 0.4261236076820623, 0.45597212989362274, 0.8805984831193984, 0.38094650276689346, 0.8824960086063224, 0.8762056525030856, 0.12904001010180927, 0.7910531219039421, 0.8568608623431296, 0.609191157481104, 0.21023361098518367, 0.6677480593332656, 0.05390918844479141, 0.8894017974042014, 0.9227662562167037, 0.7095593673531793, 0.3457144266031207, 0.21588373667235997, 0.4606340391963146, 0.6084619904604097, 0.34911221114132884, 0.7195963500512254, 0.9107630313235662, 0.603302737145989, 0.25890744697311335, 0.5310740831159212, 0.8772075219612891, 0.11897568477313389, 0.8158429842771355, 0.25757555144926175, 0.5792949967352798, 0.223184744860093, 0.9245432289567547, 0.3932122011144987, 0.3302345394026996, 0.8786753178678169, 0.046362494320836486, 0.3708124407364203, 0.42039152646213235, 0.4207990178915782, 0.015222991255795787, 0.3204779542883649, 0.2055540561362185, 0.8781958236923035, 0.12111826655334555, 0.9469278575341059, 0.09507732884788021, 0.6582351643016762, 0.06598770045982304, 0.22580296843950753, 0.4677902749522571, 0.8786521421067923, 0.4001345356548934, 0.8181149082349596, 0.9649839745092323, 0.8825480567206452, 0.4742637274848575, 0.9019774018121367, 0.439674983953517, 0.3255940258418153, 0.19255831685729963, 0.9316446339951537, 0.8896466726133728, 0.2818837193337276, 0.06599186418343446, 0.8657085183681175, 0.24852005493324497, 0.10842654623594017, 0.8722913973729814, 0.499069633491764, 0.1342912460543183, 0.5377548811851846, 0.9196197290577507, 0.19699871148711437, 0.1283950822793751, 0.1035385293367738, 0.2351378141835929, 0.854243075792854, 0.8504159942382448, 0.6454578760223926, 0.4271367538229782, 0.48770980306890005, 0.9540644177703039, 0.4768809511067771, 0.8503965059764235, 0.3177700998114613, 0.6589728408329684, 0.3221231626760005, 0.3988318756413017, 0.16068097778069504, 0.7202388192057985, 0.12923763395858792, 0.947328904465468, 0.2430090873236472, 0.9134527871150823, 0.5593917584123383, 0.8859533996885486, 0.5082674208374608, 0.7371959313584099, 0.7649305167718347, 0.9744309242269786, 0.09623957736347798, 0.967680267423952, 0.025209689604359688, 0.10295078069415323, 0.42666707069053733, 0.9113244705133795, 0.5622013906755716, 0.8069394924662249, 0.26111443436837306, 0.5106209626633605, 0.12673273002908136, 0.29847791350959507, 0.6399023263542263, 0.3566468990401646, 0.2810124833894419, 0.44550271641760797, 0.8150131485288095, 0.5980078232575767, 0.1138334647531287, 0.8618379542608194, 0.8348243051475825, 0.030875144092359204, 0.34150821959611244, 0.46644382241878146, 0.6124135635446006, 0.19809014516955306, 0.4802030015468769, 0.7890487826949212, 0.10600639469204262, 0.37705403623801254, 0.32387991317172815, 0.7115485323186809, 0.26789934543015304, 0.16631019222541074, 0.4965394931820658, 0.21020937068706727, 0.46689473182252805, 0.06934725077543924, 0.7078761244310436, 0.902805118755068, 0.008920067134655898, 0.08121208295964552, 0.707815667160107, 0.8273463961762543, 0.5610824776459197, 0.229020420160451, 0.9777003423250079, 0.1850275056885949, 0.44592151028652277, 0.35138766388353093, 0.6841173565762422, 0.4094209028031698, 0.6150752042333292, 0.9041760011460814, 0.3455385993541891, 0.7667904713271244, 0.6949629186826198, 0.47076416852797637, 0.382045619598733, 0.4986746764421157, 0.32141446133408175, 0.6142946757018587, 0.6644590110591793, 0.2876070911689947, 0.41543881220767537, 0.38703812600069654, 0.8511742568663745, 0.19999611677203935, 0.2985270229997045, 0.10813809797201424, 0.45892529464575765, 0.35677788398307675, 0.6930222802062745, 0.31556029628072696, 0.26755505612089303, 0.6524850169160122, 0.20116660959107005, 0.8410672868948211, 0.9286668560680099, 0.5468413190094514, 0.9254470015651682, 0.5184765311785545, 0.3337630233180818, 0.4798963169611203, 0.6628154301594161, 0.8053318086658168, 0.4791471682038173, 0.8320555823869676, 0.006245183443067861, 0.8364287997314388, 0.7124736566194705, 0.3841422222598797, 0.658912908632152, 0.49438407079532665, 0.11937305157413688, 0.0698410914417884, 0.44905874704247967, 0.007621505620509098, 0.9880645741409039, 0.6435325531711233, 0.9372785183579095, 0.34977383506267107, 0.7352866023687109, 0.15061345568916631, 0.4826406351895304, 0.0065575640375341495, 0.1982335297316016, 0.2749328572868937, 0.649595992552774, 0.986676939194105, 0.2244824308621502, 0.9389367346102212, 0.97416379877466, 0.09224893039953619, 0.06512520879689718, 0.9265200844186129, 0.3053262113819715, 0.9116138140117354, 0.7054919918634037, 0.0864265804148374, 0.825954670435458, 0.15320640976680974, 0.4829587868057046, 0.005315584047385152, 0.6569157307998795, 0.5534116899914913, 0.6223774563763911, 0.16433276917694023, 0.278268734167044, 0.5140130926870023, 0.8166485466069383, 0.36117484933188654, 0.24266849729310286, 0.8859656890454323, 0.2728771495252764, 0.07123120275028015, 0.1182249328565949, 0.4657866520049325, 0.02340979535855264, 0.7364139075241214, 0.5011474997433185, 0.018853219167775936, 0.03584489328103907, 0.38875472995341226, 0.8825164707948957, 0.01033463245463146, 0.7368420895265098, 0.7377521128098633, 0.888473777161356, 0.2893564768279657, 0.5212253011710458, 0.1357926112693821, 0.44901498181983723, 0.6453077536671146, 0.920482163654913, 0.8747507914834963, 0.337390175227722, 0.026947703408484017, 0.2533072381150066, 0.23908833697647125, 0.5398853619821156, 0.27515591161598063, 0.5053185787406886, 0.2364274880980048, 0.8544565401596377, 0.8387919636903511, 0.6054977949880848, 0.5756653795450455, 0.23632830377273395, 0.3501912721679857, 0.18326039002508165, 0.565225771448983, 0.38924391248951223, 0.13232199679504703, 0.23235871813977751, 0.4600107598665775, 0.3925680594608787, 0.02356356219695379, 0.46605196067646953, 0.9850198843407029, 0.9668949329762323, 0.2184399149618699, 0.1021476065889638, 0.8164457794915703, 0.5142020501455065, 0.8734518855434965, 0.45662616954423696, 0.5573341738648881, 0.9029173520113872, 0.24640039645844014, 0.8806061342949506, 0.584614086109369, 0.6035301209839816, 0.44527807338993425, 0.9773881025778408, 0.3474569328157455, 0.5565780243915278, 0.8289301996358889, 0.404237366814447, 0.9435162547968685, 0.9219803026115709, 0.6362458004439163, 0.11742148346688354, 0.889628345561435, 0.8367647307591398, 0.9736383862638203, 0.21881430435102503, 0.49702098588442917, 0.7872481489837272, 0.7620107936713495, 0.19811010274604457, 0.09798225013235289, 0.6516825953692253, 0.8442722803106075, 0.7063621556954107, 0.45128228636787915, 0.7402672418863757, 0.8327860920573655, 0.8541662575102189, 0.8774212992052866, 0.7312526701424906, 0.36287364619308266, 0.21135608413119955, 0.45199261032164534, 0.7846276594313675, 0.22368780952920805, 0.6945584388554892, 0.3161052833763385, 0.7085797718332465, 0.7413897954899655, 0.9543770109411612, 0.6469013031136648, 0.5185598438847401, 0.9316253816479942, 0.5553307438839921, 0.8987324133078476, 0.3543565448109667, 0.43879432004925983, 0.018967357734152215}
  2. Take(allRandoms, randIndex, randIndex + numRandoms - 1) → currentRandomSeeds
  3. PixelsToPoint(Corner[1], Corner[3], Corner[5], (11 + 5, 154)) → CornerLeftTable
  4. Zip((-100 + floor((n * 201))) / 10, n, Take[currentRandomSeeds, 15, 39]) → randomMult
  5. Zip(10 + floor((n * 11)), n, Take[currentRandomSeeds, 8, 32]) → randomRecip
  6. Zip(floor((n * 61)) / 10, n, First[currentRandomSeeds, 24]) → randomXH
  7. Zip(1 + floor((n * 6)), n, First[currentRandomSeeds, 24]) → problem3x
  8. Zip((round((20 + floor((n * 80))) / 5) * 5), n, Take[currentRandomSeeds, 15, 39]) → problem3y
  9. Unique(randomPoints3) → randomPoints3U
  10. Length(randomPoints3U) → lengthUnique3
  11. 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
  12. If(randomProb ≠ 2, ((42 + 2) * pixelHeightConvert), ((55 + 2) * pixelHeightConvert)) → titleHeight
  13. If(randomProb ≟ 2, 20, 100) → numMax
  14. If(randomProb ≟ 1, randomSlope1, randomProb ≟ 2, randomSlope2, 0) → randomSlope
  15. Zip((n, guideLine(n) + c / k), n, randomXH, c, randomMult, k, randomRecip) → problemPoints12
  16. Zip((round(x(n)), (round((y(n) * If[randomProb ≟ 2, 1, 0.2])) * If[randomProb ≟ 2, 1, 5])), n, problemPoints12) → problemPoints12Rounded
  17. Unique(KeepIf[y(n) < numMax, n, problemPoints12Rounded]) → problemPoints12U
  18. Length(problemPoints12U) → lengthUnique12
  19. 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
  20. If(randomProb ≟ 3, uniqueRandomPoints3, uniqueRandomPoints12) → randomPoints
  21. Sort(Zip[(round(x(n)), If[y(n) < 0, 0, y(n)]), n, randomPoints]) → randomPointsRounded
  22. If(randomProb ≟ 2, 0.2, 1) → scalingFactor
  23. Flatten(Sequence[Sequence[(n / 2, ((5 * m) * scalingFactor)), n, -6, 12], m, 0, 20]) → DragPoints
  24. Point(DragPoints) → InputPoint1
  25. Point(DragPoints) → InputPoint6
  26. Point(DragPoints) → InputPoint5
  27. Point(DragPoints) → InputPoint4
  28. Point(DragPoints) → InputPoint3
  29. Point(DragPoints) → InputPoint2
  30. Zip((x(n), y(n)), n, answerInput1) → answerInput
  31. KeepIf(¬(n ∈ answerInput), n, randomPointsRounded) → errorList
  32. Polygon({(-2.5, (105 * scalingFactor)), (-2.5, (-1 * scalingFactor)), (6.5, (-1 * scalingFactor)), (6.5, (105 * scalingFactor))}) → DragArea
  33. Sort(answerInput) → answerInputSorted
  34. Zip(n ∈ randomPointsRounded, n, answerInput) → boolCorrects
  35. Zip(abs(y(m) - y(n)), m, answerInputSorted, n, randomPointsRounded) → solutionYDifferences
  36. Zip(abs(x(m) - x(n)), m, answerInputSorted, n, randomPointsRounded) → solutionXDifferences
  37. Zip(n ≟ 0 ∧ m ≤ (2 * scalingFactor), n, solutionXDifferences, m, solutionYDifferences) → boolCorrectPoints
  38. Polygon(graphDimPoints) → graphArea
  39. 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
  40. Corner(5) → layoutAppSize
  41. Segment((0, 0), (graphDims(3), 0)) → axisX
  42. Segment((0, 0), (0, graphDims(4))) → axisY
  43. If(countQuestion ≟ 0, 1, 1 + floor((currentRandomSeeds(1) * 2))) → randomOrder
  44. Distance(Corner[sizeLabelX, 1], Corner[sizeLabelX, 2]) → numLabelXW
  45. Distance(Corner[sizeLabelY, 1], Corner[sizeLabelY, 2]) → numLabelYW
  46. Join({{tableLabel(1) + "&" + (tableLabel(2)) + "\vphantom{\frac{a}{b}}\\\hline"}, Sequence["" + (x(randomPointsRounded(n))) + "&" + (y(randomPointsRounded(n))) + "\vphantom{\large{|}}\\\hline", n, 1, 6]}) → textListForTable
  47. Sum(textListForTable) → textForTable
  48. Polygon(Sequence[Corner[textLabelX, n], n, 1, 4]) → boxAxisXLabel
  49. Polygon(Sequence[Corner[textLabelY, n], n, 1, 4]) → boxAxisYLabel
  50. Polygon(polygonCoords) → dragArea
  51. Corner(sizingText, 4) → CornerSizing
  52. Sequence(Corner[textLabelX, n], n, 1, 4) → xLabelCorners
  53. Sequence(Corner[textLabelY, n], n, 1, 4) → yLabelCorners
  54. VerticalText(textLabelY) → vertLabelY
  55. VerticalText(textLabelY) → sizeLabelYVert
  56. Distance(Corner[sizeLabelYVert, 1], Corner[sizeLabelYVert, 4]) → numVertYH
  57. Translate(PolygonCoordsStart, Vector[(2 * Vector[CornerSizing, PolygonCoordsStart])]) → StartInputPoint
  58. RemoveUndefined(Sequence[If[boolCorrectPoints(n), answerInputSorted(n)], n, 1, 6]) → correctPoints
  59. makeBox(CornerLeftTable, rowWidth, boxHeight) → hintBox
  60. If(animationSlider < 0.3, 0, animationSlider - 0.3) → animationSlider1
  61. PartitionPoint(HintPoint1, HintPoint3, animationSlider1, 1) → HintAnimate1
  62. PartitionPoint(HintPoint2, HintPoint3, animationSlider1, 1) → HintAnimate2
  63. Segment(HintPoint2, HintAnimate2 - (0.15, 0)) → hintSeg2
  64. Segment(HintPoint1, HintAnimate1 - (0, (2.4 * scalingFactor))) → hintSeg1
  65. Translate(hintBox, Vector[(0, ((-numFirstIncorrect) * rowHeight) - titleHeight)]) → hintBoxFirst
  66. Translate(hintBox, Vector[(0, ((-numFirstIncorrect) * rowHeight) - titleHeight)]) → hintBoxOutline
  67. Remove(answerInput, randomPointsRounded) → errorListInput
  68. Intersection(answerInput, randomPointsRounded) → solutionList
  69. Zip(PartitionPoint[n, m, animationSlider2, 1], n, Sort[errorListInput], m, Sort[errorList]) → solutionAnimation
  70. Sum({tableLabel(1) + "&" + (tableLabel(2)) + "\vphantom{\frac{a}{b}}\\\hline"}) → textForTitle
  71. Sum({"" + (x(randomPointsRounded(1))) + "&" + (y(randomPointsRounded(1))) + "\vphantom{\large{|}}\\\hline"}) → textForRow
  72. expandCircle(InputPoint1, 7 + (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingObject

AI Drawing Prompt Reference

Draw a scatter plot with several random points, labeled X and Y axes, and a data table listing each point's coordinates. The layout should be clear for data analysis.
The prompt above was compiled from the original drawing commands and is for reference only.