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均值、中位数和众数的交互式练习活动

均值、中位数和众数的交互式练习活动
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2020-06-24 01:55
函数数列概率统计滑块动画函数图像
该范例通过一个包含5个类别及其频数的数据表，演示了如何计算均值、中位数和众数。其中某个类别的频数未知，用户可以通过输入框调整该频数，观察三个统计量如何随之变化。核心数学概念是描述性统计中的集中趋势度量，包括均值（算术平均）、中位数（排序后中间值）和众数（出现次数最多的值）。作图要点：使用GeoGebra的Sequence、RemoveUndefined、Insert、Join等命令构建数据列表，通过Textfield和输入框（inputBox1-3）接收用户输入，利用Median、Mean、Mode函数计算统计量，并用TableText和文本对象展示数据表与问题。适合中学数学统计章节的课堂练习或自学，帮助学生直观理解不同频数对集中趋势指标的影响。

GeoGebra 命令及参数

  1. Sequence(Cell[i + 1, 1], i, 1, B3) → ListCategoryValues
  2. Sequence(Cell[i + 1, 2], i, 1, B3) → ListFrequencyValuesFromCells
  3. RemoveUndefined(ListFrequencyValuesFromCells) → ListFrequencyValuesRemovedUndefined
  4. Insert(a, ListFrequencyValuesRemovedUndefined, B4) → ListFrequencyValueswithVariable
  5. Insert("a", ListFrequencyValuesRemovedUndefined, B4) → ListFrequencyValueswithText
  6. Join({ListCategoryTitle, ListCategoryValues}) → ListCategory
  7. Textfield(targetmode) → inputBox1
  8. Textfield(targetmedian) → inputBox2
  9. Textfield(targetmean) → inputBox3
  10. Median(Take[ListCategory, 2, 5], Take[ListFrequencyNum, 2, 5]) → medianvalue1
  11. Join({ListFrequencyTitle, ListFrequencyValueswithText}) → ListFrequencyVariableText
  12. TableText({ListCategory, ListFrequencyNum}, "c|_") → Table2Solution
  13. TableText({ListCategory, ListFrequencyVariableText}, "c|_") → Table1Problem
  14. Join({ListFrequencyTitle, ListFrequencyValueswithVariable}) → ListFrequencyVariableSearch
  15. TableText({ListCategory, ListFrequencyVariableSearch}, "c|_") → Table3HiddenSearch
  16. Sum(Take[ListFrequencyVariableSearch, 2]) → totalfrequency
  17. Median(Take[ListCategory, 2, numberofcategories + 1], Take[ListFrequencyVariableSearch, 2, numberofcategories + 1]) → medianvaluesearch
  18. Sequence(If[i < numberofcategories, "+", ""], i, 1, numberofcategories) → ListAddSign
  19. Sequence(Element[ListCategoryValues, i] + "×" + (Element[ListFrequencyValueswithVariable, i] + Element[ListAddSign, i]), i, 1, numberofcategories) → CategoryFrequencyProductList
  20. Sequence(Element[MatrixAllSortedSearch, 1, i], i, 1, totalfrequency) → ListAllSortedSearch
  21. Sequence(Polygon[(i - 1, 0), (i, 0), (i, Element[ListAllSortedSearch, i]), (i - 1, Element[ListAllSortedSearch, i])], i, 1, totalfrequency) → DataVisualBar
  22. Sequence(Text[Element[ListAllSortedSearch, i], (i - 1, Element[ListAllSortedSearch * 1.1, i])], i, 1, totalfrequency) → DataVisualText
  23. Mean(Take[ListCategory, 2, numberofcategories + 1], Take[ListFrequencyVariableSearch, 2, numberofcategories + 1]) → meanvaluesearch
  24. Mode(ListAllSortedSearch) → modesearch
  25. Vector(((2 * medianposition - 1) / 2, Element[ListAllSortedSearch, totalfrequency]), ((2 * medianposition - 1) / 2, Max[Element[ListAllSortedSearch, totalfrequency] * 0.5, Element[ListAllSortedSearch, medianposition] * 1.2])) → medianpositionpointer
  26. Sum(CategoryFrequencyProductList) → TextSumCategoryFrequency