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Identifying Outliers in Scatter Plots

Identifying Outliers in Scatter Plots
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2023-05-10 18:39
Coordinate GeometryProbability & StatisticsGraphing
This activity demonstrates how to identify outliers in scatter plots. Students learn to recognize unusual data points that deviate significantly from the overall pattern, understand the impact of outliers on data analysis, and distinguish between outliers and data clusters. The construction uses GeoGebra commands including RandomUniform for generating random coordinates, Sequence and Zip for data sequence construction, Polygon and Segment for graphical elements, and Text for annotations. Suitable for grades 6-8, this resource helps students develop fundamental statistical reasoning skills and learn to analyze bivariate data effectively.

GeoGebra Commands & Parameters

  1. RandomUniform(0, 0.99, 200) → allRandomSeeds, {0.7958563944291628, 0.3915624918818961, 0.2932294420836522, 0.7401431704012463, 0.5724260744306325, 0.4221525938901191, 0.34109160907200825, 0.1920062173159564, 0.06459378524871139, 0.6751254787774517, 0.32062091846183877, 0.5720348974994817, 0.22331925897635088, 0.096843629867881, 0.18811562796390063, 0.8203698204783221, 0.6687153478476997, 0.08261124973631181, 0.858568555031248, 0.20178749931964832, 0.874767751975692, 0.3752216590567491, 0.6502463678419537, 0.07006907993764211, 0.8881350399719284, 0.6877211873958065, 0.7660107840972353, 0.8597247594222645, 0.48882052213645943, 0.9845847202995538, 0.43172701145374964, 0.7749081018924836, 0.03272417760878359, 0.26326178391670785, 0.07228980774550432, 0.03983799795433378, 0.43173726117095146, 0.6167533302978182, 0.6344213618534845, 0.6154653387901594, 0.6561336846816218, 0.6275180858869077, 0.7324549204805334, 0.6234792288537817, 0.766542110089728, 0.823583044270964, 0.20881648558938223, 0.501042060352078, 0.1687490173529191, 0.4692472069838345, 0.15485300822112405, 0.7778757146537608, 0.8639873850970144, 0.7352180231402488, 0.8700271087595832, 0.10149074071876378, 0.7802076461902923, 0.7464089528112822, 0.05831069845703875, 0.7064577245020829, 0.7261068710146533, 0.9199531034376868, 0.5998565154992634, 0.8896653388235399, 0.6194083045386612, 0.5112508125444578, 0.0037127433237835526, 0.20549177676785033, 0.6440387996790884, 0.30207108796431986, 0.6434688791755673, 0.6727357478348958, 0.40744229203677385, 0.861864575705091, 0.6322816045965117, 0.829011828321198, 0.029297719810629987, 0.0015228640392135962, 0.6667271636389044, 0.4681084424090525, 0.9063759752366872, 0.3178316442985397, 0.3103627117189817, 0.9715401976612131, 0.4651751323890168, 0.4868172665175646, 0.5477518272262617, 0.27719584300321637, 0.27431458986255963, 0.8050742765065133, 0.8080200889537797, 0.1455905880889658, 0.4524487545051796, 0.4599880047523782, 0.7937546807712456, 0.15777624158916556, 0.7046767743342622, 0.12252997231276885, 0.2662472579581525, 0.2684455660584788, 0.26107990954340693, 0.20000478458426962, 0.7517028741538923, 0.4731865646071906, 0.3151096071688003, 0.47076617087072503, 0.4650977504439952, 0.9302003076969629, 0.897078545236155, 0.45849583389272625, 0.9588672224995374, 0.3940903854577935, 0.9489738507998193, 0.5001523888535302, 0.21254021836316322, 0.7125651825333108, 0.25121610767710517, 0.12914905868235727, 0.3868102079874485, 0.9060630714392015, 0.42982910804351204, 0.9537071392452489, 0.3813427049349712, 0.04541912757159863, 0.6337654114070467, 0.119658898092048, 0.369867698728792, 0.013736307778379982, 0.4268484536057839, 0.7672366049161309, 0.828790746785832, 0.3456060488252243, 0.5669475049998695, 0.3125862159416647, 0.526679639537814, 0.7497445253821092, 0.9465924165087093, 0.3368824433210023, 0.37154408442406855, 0.3699664321067477, 0.38426515170810605, 0.5089982898281532, 0.9408238814490792, 0.37421483323730037, 0.23407182419861483, 0.20169585156131414, 0.3454365259265787, 0.8620964665737362, 0.9434025041590448, 0.6562561985053055, 0.36410830891567497, 0.6780431959932847, 0.30352933258129783, 0.4663550099872679, 0.6475237779407599, 0.1098266489195119, 0.7468708655756197, 0.8588166464308096, 0.2535756306952432, 0.3506986715614222, 0.7468692928921373, 0.5966431442216774, 0.175183988032395, 0.8979123118545231, 0.9720799911198285, 0.9284155925995324, 0.940775587674635, 0.910798117341396, 0.34516547722753954, 0.4578044491752583, 0.9545753182858937, 0.08792799313471682, 0.440014843961109, 0.4675007741791743, 0.23935939358061237, 0.5251934528243069, 0.5161766455688401, 0.7433950042938801, 0.6482558916496483, 0.6148580961587056, 0.419197340804247, 0.7272802044003266, 0.0945510069298192, 0.7798135700107173, 0.9182994835011812, 0.19974578346205316, 0.9492699809923367, 0.79737581002263, 0.7991128170773751, 0.8192540671404379, 0.3955497920028327, 0.23300344408647305, 0.54888848777437, 0.16865511746150427, 0.21650598151695236, 0.25630259990909265, 0.10478084240361232, 0.9065971245340948, 0.8994195876317771, 0.30960207110173954}
  2. If(maxRandIndex > numRandoms, Take[allRandomSeeds, maxRandIndex - numRandoms, maxRandIndex], Take[allRandomSeeds, 1, numRandoms]) → currentRandomSeeds
  3. If(regSlope < 0, 8.5, If[regSlope > 0, 1.5, 2]) → regIntercept
  4. Insert((0.5 * 20 / divisorY), Sequence[floor(((currentRandomSeeds(numPoints - numOutliers + 1 + k) - 0.5) * 20)) / divisorY, k, 1, numPoints - 1], 10) → randomListY
  5. KeepIf(x > 0, randomListY) → posY
  6. IndexOf((0.5 * 20 / divisorY), randomListY) → onboardingIndex
  7. If(currentRandomSeeds(1) > 0.5, true, false) → isCluster
  8. If(isCluster, round((currentRandomSeeds(1) * 7) + 1), 5) → clusterLocation
  9. If(isCluster, 11, 3) → divisorX
  10. If(isCluster, Sequence[clusterLocation + round(((currentRandomSeeds(k + 1) - 0.5) * 25)) / divisorX, k, 1, numPoints], Sequence[((k + ((-1)^(k + 1) * currentRandomSeeds(k + 1))) * (maxX - 1) / numPoints), k, 1, numPoints]) → randomListX
  11. Sequence((Element[randomListX, k], (regSlope * Element[randomListX, k]) + regIntercept + Element[randomListY, k]), k, 1, numPoints) → pointsList
  12. If(abs(abs(regSlope) - 0.5) ≤ 0.1, (regSlope * (-1 / 2)), If[regSlope ≠ 0, (regSlope * (-1)), 0.3]) → outlierSlope
  13. Sequence(currentRandomSeeds(k) / 2 + k, k, 1, 9) → outlierX, {1.3979281972145814, 2.1957812459409483, 3.1466147210418263, 4.370071585200623, 5.286213037215316, 6.21107629694506, 7.170545804536004, 8.096003108657978, 9.032296892624355}
  14. Zip((k, (outlierSlope * k) + outlierIntercept), k, outlierX) → outlierOptions
  15. KeepIf(Distance[A, ClosestPoint[pointsList, A]] > outlierMin, A, outlierOptions) → outlierPoints
  16. Element(outlierPoints, Length[outlierPoints]) → Outlier2
  17. Element(outlierPoints, 1) → Outlier1
  18. Element({{Outlier1}, {Outlier1, Outlier2}}, numOutliers) → allOutliers
  19. Join({pointsList, allOutliers}) → allPoints
  20. Take(inputCurrent, 1, numPoints) → clusterBooleanList
  21. Take(inputCurrent, numPoints + 1, numPoints + numOutliers) → outlierBooleanList
  22. Corner(5) → layoutAppSize
  23. Polygon({(-0.5, -0.5), (-0.5, maxY + 0.5), (maxX + 0.5, maxY + 0.5), (maxX + 0.5, -0.5)}) → viewbox
  24. Element(pointsList, 1) → point1
  25. Element(pointsList, 2) → point2
  26. Element(pointsList, 3) → point3
  27. Element(pointsList, 4) → point4
  28. Element(pointsList, 5) → point5
  29. Element(pointsList, 6) → point6
  30. Element(pointsList, 7) → point7
  31. Element(pointsList, 8) → point8
  32. Element(pointsList, 9) → point9
  33. Element(pointsList, 10) → point10
  34. Element(pointsList, 11) → point11
  35. Element(pointsList, 12) → point12
  36. Element(pointsList, 13) → point13
  37. Element(pointsList, 14) → point14
  38. Element(pointsList, 15) → point15
  39. Element(pointsList, 16) → point16
  40. Element(pointsList, 18) → point18
  41. Element(pointsList, 19) → point19
  42. Element(pointsList, 17) → point17
  43. Segment((0, 0), (0, maxY + 0.5)) → yAxisLine
  44. Segment((0, 0), (maxX + 0.5, 0)) → xAxisLine
  45. Text("y", (0.05, maxY + 0.6), true, true, 0, 1) → lblY
  46. Polygon({(-0.5, -0.5), (-0.5, maxY), (maxX, maxY), (maxX, -0.5)}) → ShadedBox
  47. RemoveUndefined(Sequence[If[clusterBooleanList(A), allPoints(A)], A, 1, numPoints]) → selectedClusterPoints
  48. RemoveUndefined(Sequence[If[outlierBooleanList(A), allOutliers(A)], A, 1, numOutliers]) → selectedOutliers
  49. Join({selectedClusterPoints, selectedOutliers}) → allSelectedPoints
  50. Text("x", (maxX + 0.6, 0.1), true, true, 1, 0) → lblX

AI Drawing Prompt Reference

Draw a scatter plot with randomly generated data points and possible outlier points. Include axes and grid lines for reference. The construction order is: first generate random coordinates, identify outliers that deviate from the overall trend, then plot all points on the coordinate system, marking outliers differently.
The prompt above was compiled from the original drawing commands and is for reference only.