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Step-by-Step Modified Boxplot Construction

Step-by-Step Modified Boxplot Construction
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2014-04-05 02:18
Geometric ConstructionGraphing
In collections Statistics Step Through Applets
This example demonstrates how to construct a modified boxplot step-by-step. It guides students through the interactive process of building a boxplot. Key math concepts involved include dataset analysis, quartiles (Q1, Q3), median, interquartile range (IQR), and outlier handling. The construction utilizes GeoGebra commands like Element, Sequence, Min, Max, If, Q3, Q1, Sort, Median, Intersection, CountIf, KeepIf, Segment, Midpoint, Union, along with objects such as DS1, DS2, DS3, DS4, dataset, QHi, QLo, IQR. Suitable for high school students learning data visualization and statistical analysis.

GeoGebra Commands & Parameters

  1. Element(DSSq, dataset) → DS0
  2. Element(PrmSq, seed) → Rate
  3. Sequence(Element[DS0, Mod[4 + (Rate * k), 20] + 1], k, 1, size) → Sample
  4. Min(Sample) → OldMin
  5. Max(Sample) → OldMax
  6. If((5 * SFLB) ≤ SFUB, (5 * SFLB), If[(2 * SFLB) ≤ SFUB, (2 * SFLB), SFLB]) → SF
  7. Element(AcSq, dataset) → Acc
  8. Q3(Sample) → QHi
  9. Q1(Sample) → QLo
  10. Sequence(k, k, OldMin, OldMax, Acc) → Domain
  11. Sort(Intersection[Domain, Sample]) → Range
  12. Median(Sample) → Med1
  13. Sequence(k, k, (ceil(LoFn / Acc) * Acc), (floor(UpFn / Acc) * Acc), Acc) → Middle
  14. Intersection(Sample, Middle) → GoodData
  15. Min(GoodData) → NewMin
  16. CountIf(x < LoFn, Range) → LfOtlrCntRng
  17. Max(GoodData) → NewMax
  18. CountIf(x > UpFn, Range) → RtOtlrCntRng
  19. KeepIf(x > UpFn, Range) → DmAbFn
  20. CountIf(x ≤ OldMax, Range) → RngCnt
  21. Segment(AxLE, AxRE) → axis
  22. Segment(NMinT, NMinB) → nwmin
  23. Midpoint(nwmin) → NMinM
  24. Segment(QLoT, QLoB) → qlo
  25. Segment(MedT, MedB) → med
  26. Midpoint(qlo) → QLoM
  27. Segment(NMinM, QLoM) → lfwh
  28. Segment(QHiT, QHiB) → qhi
  29. Segment(QLoT, QHiT) → boxtop
  30. Segment(QLoB, QHiB) → boxbot
  31. Segment(NMaxT, NMaxB) → nwmax
  32. Midpoint(nwmax) → NMaxM
  33. Midpoint(qhi) → QHiM
  34. Segment(QHiM, NMaxM) → rtwh
  35. KeepIf(x < LoFn, Range) → LfOtlrVls
  36. CountIf(x > UpFn, Sample) → RtOtlrCnt
  37. CountIf(x < LoFn, Sample) → LfOtlrCnt
  38. KeepIf(x < LoFn, Range) → DmBlFn
  39. Element(DDSq, dataset) → DD0
  40. Segment(TbUL, TbUR) → tbtp
  41. Segment(TbML, TbMR) → tbmd
  42. Segment(TbLL, TbLR) → tbbt
  43. Segment(TbUL, TbLL) → tblf
  44. Segment(TbUR, TbMR) → tbrt
  45. Sequence(Segment[(TbLf + (k * TbCW), TbTp), (TbLf + (k * TbCW), TbTp - (2 * TbCH))], k, 1, DtRL2) → TbDLSq
  46. Sequence(Text[k, (adp(k) - 1, AxHt - 0.07)], k, AxMin, AxMax, SF) → AxLbSq
  47. Sequence(Segment[(adp(k), AxHt + 0.01), (adp(k), AxHt - 0.01)], k, AxMin, AxMax, SF) → AxTcSq
  48. Sequence((adp(Element[DmAbFn, k]), AxHt + 0.2), k, 1, RtOtlrCntRng) → RtOtlr
  49. Sequence((adp(Element[LfOtlrVls, k]), AxHt + 0.2), k, 1, LfOtlrCntRng) → LfOtlrSq
  50. Sequence(Text[Element[Sample, k], (TbLf - 5 + (k * 6), TbTp - 0.08)], k, 1, DtRL1) → DRw1
  51. Sequence(Text[Element[Sample, k + DtRL1], (TbLf - 5 + (k * 6), TbTp - TbCH - 0.08)], k, 1, DtRL2) → DRw2
  52. If(QLo < 0, IQRNQL, IQRPQL) → IQRCmTx
  53. KeepIf(x > UpFn, Range) → RtOtlrVls
  54. Union(RtOtlrVls, LfOtlrVls) → Outliers
  55. Element(UntSq, dataset) → Unt0
  56. Element(TtlSq, dataset) → Ttl0

AI Drawing Prompt Reference

Draw a modified boxplot to illustrate dataset analysis, quartiles, median, interquartile range, and outlier handling. Start by plotting data points, identifying the minimum and maximum values, then locate the quartiles and median, draw the box and whiskers, and finally mark the outliers. The process should demonstrate the step-by-step construction of the boxplot.
The prompt above was compiled from the original drawing commands and is for reference only.