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Histogram Analysis Problems

Histogram Analysis Problems
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2015-08-13 23:57
Probability & StatisticsGraphing
This GeoGebra applet presents various questions about a few histograms. Checking the check boxes reveals the answers. The example involves histogram construction and analysis, using commands such as Sequence, Element, Max, Min, If, KeepIf, Sort, CountIf, Segment, Append, TableText, VerticalText, and Text. Suitable for high school mathematics, particularly in statistics and probability.

GeoGebra Commands & Parameters

  1. Sequence(Mod[11 + (k * 29), 59] + 1, k, 0, 59) → OpSq1
  2. Element(OpSq1, Seed) → OpNm1
  3. Element(AcSq, Op0) → Acc
  4. Element(RtSq, Mod[Seed, 8] + 1) → Rate
  5. Sequence(Mod[(Rate * k) + Strt, 23] + 1, k, 0, 22, 1) → OpSq2
  6. Element(DSSq, Op0) → DS0
  7. Sequence(Element[DS0, Element[OpSq2, k]], k, 1, Size) → Sample
  8. Max(Sample) → SmpMx1
  9. Min(Sample) → SmpMn1
  10. If(C0 ≤ UB, 0, If[C1 ≤ UB, 0, If[C2 ≤ UB, 1, If[C3 ≤ UB, 2, 3]]]) → CWAcc
  11. Max(Acc, CWAcc) → QFTAcc
  12. If(C0 ≤ UB, C0, If[C1 ≤ UB, C1, If[C2 ≤ UB, C2, If[C3 ≤ UB, C3, C4]]]) → ClWd
  13. Sequence(SmpMn1 + (k * ClWd), k, 0, NmCls - 1) → LCLSq1
  14. Element(LCLSq1, 2) → LCL2
  15. Sequence(UCL1 + (ClWd * k), k, 0, NmCls - 1) → UCLSq1
  16. Sequence(CountIf[Element[LCLSq1, k] ≤ x ≤ Element[UCLSq1, k], Sample], k, 1, NmCls) → FrqSq
  17. Max(FrqSq) → FrqMx1
  18. If(FrqMx1 > 12, 3, If[FrqMx1 > 6, 2, 1]) → VAScl
  19. Sequence(7.95 - (k * 0.75), k, 0, 3) → LHSq
  20. Element(LHSq, 4) → LH3
  21. If(Mod[Size, 3] ≟ 2, ceil(Size / 3), floor(Size / 3)) → RL2
  22. Element(LHSq, 2) → LH1
  23. Element(LCLSq1, 1) → SmpMn0
  24. Element(Places, Op0) → DP
  25. Sequence(k, k, 1, 19) → StrSq
  26. KeepIf(floor(20 / x) ≠ 20 / x, StrSq) → RlPrSq
  27. Element(GrphTtSq, Op0) → TypeLabel
  28. Element(DDSq, Op0) → GD0
  29. Sort(Sample) → SrtSq
  30. CountIf(x > 0, RtSq) → RateNo
  31. Element(SclSq, Op0) → Scale
  32. Segment(RE, LE) → HAx
  33. Element(TSSq, Op0) → TS
  34. Element(AxTtlSq, Op0) → HALb
  35. Sequence(SmpMn1 + (k * ClWd), k, 0, NmCls - 2) → LCLSq2
  36. Append(SmpMn1, LCLSq2) → LCLSq0
  37. Sequence(UCL1 + (ClWd * k), k, 0, NmCls - 2) → UCLSq2
  38. Append(UCL1, UCLSq2) → UCLSq0
  39. Sequence(Segment[(HAMn + ((HAScl * ClWd) * k), VAMn - 0.1), (HAMn + ((HAScl * ClWd) * k), VAMn + 0.1)], k, 0, NmCls, 1) → HTc
  40. Segment(LE, VAE) → VAx
  41. If(VAScl ≟ 3, (ceil(FrqMx1 / 3) * 3), If[VAScl ≟ 2, (ceil(FrqMx1 / 2) * 2), FrqMx1]) → FrqMx2
  42. Element(LCLSq1, 1) → LCL1
  43. Element(LHSq, 3) → LH2
  44. Element(LHSq, 1) → LH0
  45. Element(PrtBSq, Mod[OpNm1, 4] + 1) → PrtB
  46. Min(FrqSq) → FrqMn
  47. Sequence(Text["[" + (Element[LCLSq1, k]) + "," + (Element[UCLSq1, k]) + "]"], k, 1, NmCls) → ClsSq
  48. Sequence(If[Element[FrqSq, k] ≟ FrqMx1, k, 0], k, 1, NmCls) → MxClsLc
  49. KeepIf(x > 0, MxClsLc) → MxPs
  50. CountIf(x > 0, MxPs) → FrqCntMx
  51. Sequence(Element[ClsSq, Element[MxPs, k]], k, 1, FrqCntMx) → MxCls
  52. Sequence(If[Element[FrqSq, k] ≟ FrqMn, k, 0], k, 1, NmCls) → MnCls
  53. KeepIf(x > 0, MnCls) → MnPs
  54. CountIf(x > 0, MnPs) → FrqCntMn
  55. Sequence(Element[ClsSq, Element[MnPs, k]], k, 1, FrqCntMn) → MnClsLc
  56. TableText({MxCls}, "hl") → AnsB1
  57. TableText({MnClsLc}, "hl") → AnsB2
  58. Element(AnBSq, Mod[OpNm1, 4] + 1) → AnsB
  59. VerticalText("Frequency", (0.2, -2)) → VAxLb
  60. Sequence(Text[k, (HAMn - 1.1, adp2(k)) - 0.2], k, 0, FrqMx2, VAScl) → VLbs
  61. Sequence(Text[LCL1 + (k * ClWd), (adp1(LCL1 + (k * ClWd)) - 0.6, VAMn - 0.9)], k, 0, NmCls) → HALb_2
  62. Text("c) What is the maximum data value?") → PrtC2
  63. Sequence(Mod[8 + (k * 23), 59] + 1, k, 0, 59) → OpSq3
  64. Element(OpSq3, Seed) → OpNm3
  65. Text("c) What is the minimum data value?") → PrtC1
  66. Element(PrtCSq, ChC) → PrtC
  67. Text((("The minimum data value is about " * SmpMn0) * ".")) → AnsC1
  68. Text((("The maximum data value is about " * SmpMx2) * ".")) → AnsC2
  69. If(ChC ≟ 1, AnsC1, AnsC2) → AnsC
  70. Sequence((adp1(LCL1 + (ClWd * (k - 1))), adp2(Element[FrqSq, k])), k, 1, NmCls) → BrULSq
  71. Sequence((adp1(LCL1 + (ClWd * k)), adp2(Element[FrqSq, k])), k, 1, NmCls) → BrURSq
  72. Sequence((adp1(LCL1 + ((k - 1) * ClWd)), VAMn), k, 1, NmCls) → BrLLSq
  73. Sequence((adp1(LCL1 + (k * ClWd)), VAMn), k, 1, NmCls) → BrLRSq
  74. Sequence(Polygon[Element[BrLLSq, k], Element[BrULSq, k], Element[BrURSq, k], Element[BrLRSq, k]], k, 1, NmCls) → BrSq
  75. Sequence(Segment[Element[BrULSq, k], Element[BrURSq, k]], k, 1, NmCls) → BrTpSq
  76. Sequence(Segment[Element[BrULSq, k], Element[BrLLSq, k]], k, 1, NmCls) → BrLSSq
  77. Sequence(Segment[Element[BrURSq, k], Element[BrLRSq, k]], k, 1, NmCls) → BrRSSq
  78. Sequence(Segment[Element[BrLLSq, k], Element[BrLRSq, k]], k, 1, NmCls) → BrBtSq
  79. Sequence(Segment[(HAMn - 0.2, adp2(k)), (HAMn, adp2(k))], k, 0, FrqMx2, VAScl) → Vtcs
  80. Sequence(Segment[(HAMn, adp2(k)), (HAMx, adp2(k))], k, 0, FrqMx2, VAScl) → HGrd