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Boxplot Construction Example

Boxplot Construction Example
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2016-10-05 03:59
Probability & StatisticsGeometric ConstructionGraphing
In collections Numeracy Practice
This example demonstrates how to construct a boxplot using GeoGebra, visually representing data distribution characteristics. Key mathematical concepts involved include statistical measures such as median, quartiles, and range, along with data sorting and interval partitioning. The construction leverages GeoGebra commands/objects like Element, Sequence, Min, Max, If, Q3, Q1, Sort, Median, Intersection, CountIf, KeepIf, Segment, Midpoint, Union, and objects including seed, PrmFct, Cmpst, Nmbr1 to Nmbr4, Chc4 to Chc1, Size, DD5 to DD1, Unt5 to Unt1, Ttl5 to Ttl1, Strt, Rate, OpSq, DS1 to DS5, DSSq, DataSet, DS0. It is suitable for high school mathematics courses in statistics and probability, serving as a teaching demonstration or for student exploratory learning.

GeoGebra Commands & Parameters

  1. Element(RPSq, Chc3) → Rate
  2. Sequence(Mod[Strt + (Rate * k), 23] + 1, k, 0, 22, 1) → OpSq
  3. Element(DSSq, DataSet) → DS0
  4. Sequence(Element[DS0, Element[OpSq, k]], k, 1, Size) → Sample
  5. Min(Sample) → OldMn
  6. Max(Sample) → OldMx
  7. If((5 * AxUntLB) ≤ AxUntUB, (5 * AxUntLB), If[(2 * AxUntLB) ≤ AxUntUB, (2 * AxUntLB), AxUntLB]) → AxUnt
  8. Element(AcSq, DataSet) → Acc
  9. Q3(Sample) → SmpQ3
  10. Q1(Sample) → SmpQ1
  11. Sequence(k, k, OldMn, OldMx, Acc) → Domain
  12. Sort(Intersection[Domain, Sample]) → Range
  13. Median(Sample) → SmpMdn
  14. Sequence(k, k, (ceil(LoFn / Acc) * Acc), (floor(UpFn / Acc) * Acc), Acc) → Middle
  15. Intersection(Sample, Middle) → GoodData
  16. Min(GoodData) → NwMn
  17. CountIf(x < LoFn, Range) → LfOtlrCntRng
  18. Max(GoodData) → NwMx
  19. CountIf(x > UpFn, Range) → RtOtlrCntRng
  20. KeepIf(x > UpFn, Range) → DmAbFn
  21. CountIf(x ≤ OldMx, Range) → RngCnt
  22. Segment(AxLE, AxRE) → axis
  23. Segment(NMinT, NMinB) → nwmin
  24. Midpoint(nwmin) → NMinM
  25. Segment(QLoT, QLoB) → qlo
  26. Segment(MedT, MedB) → med
  27. Midpoint(qlo) → QLoM
  28. Segment(NMinM, QLoM) → lfwh
  29. Segment(QHiT, QHiB) → qhi
  30. Segment(QLoT, QHiT) → boxtop
  31. Segment(QLoB, QHiB) → boxbot
  32. Segment(NMaxT, NMaxB) → nwmax
  33. Midpoint(nwmax) → NMaxM
  34. Midpoint(qhi) → QHiM
  35. Segment(QHiM, NMaxM) → rtwh
  36. KeepIf(x < LoFn, Range) → LfOtlrVls
  37. CountIf(x > UpFn, Sample) → RtOtlrCnt
  38. CountIf(x < LoFn, Sample) → LfOtlrCnt
  39. KeepIf(x < LoFn, Range) → DmBlFn
  40. Element(DDSq, DataSet) → DD0
  41. Segment(TbUL, TbUR) → tbtp
  42. Segment(TbML, TbMR) → tbmd
  43. Segment(TbLL, TbLR) → tbbt
  44. Segment(TbUL, TbLL) → tblf
  45. Segment(TbUR, TbMR) → tbrt
  46. Sequence(Segment[(TbLf + (k * TbCW), TbTp), (TbLf + (k * TbCW), TbTp - (2 * TbCH))], k, 1, DtRL2) → TbDLSq
  47. Sequence(Text[k, (adp(k) - 1, AxHt - 0.07)], k, AxMn, AxMx, AxUnt) → AxLbSq
  48. Sequence(Segment[(adp(k), AxHt + 0.01), (adp(k), AxHt - 0.01)], k, AxMn, AxMx, AxUnt) → AxTcSq
  49. Sequence((adp(Element[DmAbFn, k]), AxHt + 0.2), k, 1, RtOtlrCntRng) → RtOtlr
  50. Sequence((adp(Element[LfOtlrVls, k]), AxHt + 0.2), k, 1, LfOtlrCntRng) → LfOtlrSq
  51. KeepIf(x > UpFn, Range) → RtOtlrVls
  52. Union(RtOtlrVls, LfOtlrVls) → Outliers
  53. Element(UntSq, DataSet) → Unt0
  54. Element(TtlSq, DataSet) → Ttl0
  55. If(WhLnRt > WhLnLf + (0.05 * ScFc), 1, If[WhLnLf > WhLnRt + (0.05 * ScFc), 2, If[BxLnRt > BxLnLf + (0.05 * ScFc), 3, If[BxLnLf > BxLnRt + (0.05 * ScFc), 4, 5]]]) → ShpNmb
  56. Sequence(Text[Element[Sample, k + DtRL1], (TbLf - 5.5 + (k * 6), TbTp - TbCH - 0.08)], k, 1, DtRL2) → DRw2
  57. Sequence(Text[Element[Sample, k], (TbLf - 5.5 + (k * 6), TbTp - 0.08)], k, 1, DtRL1) → DRw1

AI Drawing Prompt Reference

Create a boxplot to visually represent data distribution characteristics, highlighting statistical measures like median, quartiles, and range. Identify the minimum and maximum values in the dataset, then determine the first quartile (Q1) and third quartile (Q3). Draw the box on the axis between Q1 and Q3, with a line inside representing the median. Extend whiskers from the box to the minimum and maximum values. Label the axis with appropriate intervals.
The prompt above was compiled from the original drawing commands and is for reference only.