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Bar Graph vs Histogram

Bar Graph vs Histogram
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2018-05-08 02:56
Probability & StatisticsGraphing
This example contrasts bar graphs and histograms to demonstrate different ways of representing data. Key mathematical concepts include frequency distribution, statistical measures (such as mode and median), and data visualization. GeoGebra commands like Element, Random, Sequence, and Frequency are used to construct the charts. Suitable for middle school and above students to learn data statistics and chart representation.

GeoGebra Commands & Parameters

  1. Element({"continuous", "discrete", "discrete", "discrete", "continuous", "continous", "discrete"}, ImgNum) → datatypeText
  2. Random(1, 3) → Object
  3. Random(LowestValue + 4, LowestValue + 5) → DiscreteHighest
  4. Random(LowestValue + 10, LowestValue + 12) → ContHighest
  5. Sequence(Random[LowestValue, DiscreteHighest], i, 1, 12) → DiscreteList
  6. Frequency(DiscreteList) → DiscreteFrequency
  7. Sequence(((Random[LowestValue, ContHighest] * 10) + (Random[0, 1] * 5)) / 10, i, 1, 12) → ContList
  8. Frequency(ContList) → ContFrequency
  9. If(datatype ≟ 0, ContList, DiscreteList) → DataList
  10. If(datatype ≟ 0, ContFrequency, DiscreteFrequency) → FreqList
  11. Sort(Unique[DataList]) → UniqueList
  12. If(datatype ≟ 0, ContHighest, DiscreteHighest) → HighestValue
  13. Max(FreqList) → MaxFreq
  14. Min(DataList) → Low
  15. Max(DataList) → High
  16. If(datatype ≟ 1, 0.7, 0.3) → BarWidth
  17. BarChart(UniqueList, FreqList, BarWidth) → BarGraph
  18. LaTeX("\textbf{Data\text{:}}\ 8,\,6.5,\,12,\,7.5,\,14,\,12,\,7.5,\,10.5,\,11,\,14.5,\,9,\,7") → Data1
  19. LaTeX("\textbf{Data\text{:}}\ 8,\,8,\,13.5,\,16,\,11,\,18,\,19,\,18,\,13,\,14.5,\,19.5,\,14") → Data2
  20. LaTeX("\textbf{Data\text{:}}\ 11,\,8.5,\,10.5,\,5.5,\,6.5,\,10,\,3.5,\,7.5,\,11,\,8,\,11,\,11.5") → Data3
  21. LaTeX("\textbf{Data\text{:}}\ 4,\,10.5,\,9,\,12,\,11.5,\,15.5,\,14,5,\,5.5,\,7,\,13.5,\,12") → Data5
  22. LaTeX("\textbf{Data\text{:}}\ 3,\,1.5,\,4,\,2.5,\,9,\,2.5,\,10,\,9.5,\,1,\,12,\,12,\,9") → Data4
  23. LaTeX("\textbf{Data\text{:}}\ 12,\, 14.5,\, 19.5,\, 10.5,\, 10.5,\, 16.5,\, 10.5,\, 17,\,11.5,\, 12.5,\, 19,\, 20") → Data6
  24. LaTeX("\textbf{Data\text{:}}\ 4,\, 4,\, 4,\, 1,\, 3,\, 3,\, 2,\, 4,\,2,\, 3,\, 3,\, 3") → Data7
  25. If(ImgNum ≟ 1, LaTeX[Data1], If[ImgNum ≟ 2, LaTeX[Data2], If[ImgNum ≟ 3, LaTeX[Data3], If[ImgNum ≟ 4, LaTeX[Data4], If[ImgNum ≟ 5, LaTeX[Data5], If[ImgNum ≟ 6, LaTeX[Data6], LaTeX[Data7]]]]]]) → DataListDisplay
  26. Sort(ContList) → sortedContList
  27. LaTeX("Continuous\ data\ often\ consists\ of\ a\ wide\ variety\ of\ values.\, This\ results\ in\ many\ frequencies\\ of\ 1\ and\ means\ that\ the\ bar\ graph\ may\ not\ be\ as\ helpful\ as\ the\ histogram.") → SummarText
  28. LaTeX("\textbf{Instructions\text{:}}\ Use\ the\ buttons\ to\ display\ different\ representations\ of\ the\ data\ set.\, then\ use\ the\ \textbf{Summary}\ button\ to\\ check\ your\ thinking.") → Instructions2
  29. LaTeX("weight\ of\ chairs\ at\ a\ restaurant") → Data1Description
  30. LaTeX("length\ of\ different\ bedrooms") → Data2Description
  31. LaTeX("length\ of\ triangle\ bases") → Data3Description
  32. LaTeX("height\ of\ trees\ in\ the\ park") → Data5Description
  33. LaTeX("volume\ of\ water\ held\ in\ containers") → Data4Description
  34. LaTeX("weight\ of\ children") → Data6Description
  35. Element({Data1Description, Data2Description, Data3Description, Data4Description, Data5Description, Data6Description}, ImgNum) → DataDescription
  36. LaTeX("The\ data\ set\ below\ represents\ " + DataDescription + "\ and\ is\ continuous\ data.\\ Explore\ different\ representations\ of\ the\ data\ set.\ Which\ representation\ is\ more\ helpful?") → Instructions