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Review

Learn about graphical representation techniques for quantitative data, including histograms, stem and leaf plots, and dot plots. Understand how to summarize and visualize numerical data effectively.

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Review

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  1. Review • Sections 2.1, 2.2, 1.3, 1.4, 1.5, 1.6 in text

  2. Quantitative Data (Graphical)

  3. Quantitative Data (Graphical) • This is numerical data • We may describe quantitative data using the same methods as qualitative by breaking our numerical data into classes. That is 20-30, 30-40, 40-50, 50-60.

  4. Quantitative Data (Graphical) • This is numerical data • We may describe quantitative data using the same methods as qualitative by breaking our numerical data into classes. That is 20-30, 30-40, 40-50, 50-60. • Histograms, stem and leaf plots and dot plots are other common methods of displaying quantitative data.

  5. Histograms • A histogramis a bar graph where you use intervals for your data class. • The following histogram summarizes the NBA payroll. You should note that the are adjacent to one another.

  6. NBA Payroll

  7. Stem and Leaf, and Dot Plots • Notice in the histogram on the previous page we lose some information. That is we don’t know exactly what each team is paying in salary just how many are paying in the range of 1.885 million dollars.

  8. Stem and Leaf, and Dot Plots • Notice in the histogram on the previous page we lose some information. That is we don’t know exactly what each team is paying in salary just how many are paying in the range of 1.885 million dollars. • A stem and leaf plot is a graphical device which uses numbers so that no information is lost.

  9. Stem and Leaf, and Dot Plots • A stem and leaf plot is a graphical device which uses numbers so that no information is lost. • The technique separates each data point into two numbers, the stem (the leading digit) and the leaves.

  10. Stem and Leaf, and Dot Plots • The technique separates each data point into two numbers, the stem (the leading digit) and the leaves. • In a dot plot we start with a number line of all possible values for the data. Each data point is represented with a dot above the appropriate number. If a number appears more than once in your data you build a tower of dots above that point.

  11. Example • Here is a list of exam scores: 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 Construct a histogram (with interval size 10 starting at 24), a stem and leaf diagram and a dot plot .

  12. Histogram of Exam Scores

  13. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  14. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  15. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  16. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  17. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  18. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  19. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  20. Stem and Leaf Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  21. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96

  22. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 30 40 50 60 70 80 90 100

  23. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 30 40 50 60 70 80 90 100

  24. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 30 40 50 60 70 80 90 100

  25. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 30 40 50 60 70 80 90 100

  26. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 30 40 50 60 70 80 90 100

  27. Dot Plot of Exam Scores 88, 82, 89, 70, 85, 63, 100, 86, 67, 39, 90, 96, 76, 34, 81, 64, 75, 84, 89, 96 30 40 50 60 70 80 90 100

  28. Summation Notation Here is a typical (small) data set: 2 7 1 3 2

  29. Summation Notation Here is a typical (small) data set: 2 7 1 3 2 So we can talk about a general data set we let:

  30. Summation Notation So we can talk about a general data set we let: In general for a sample of n points of data we call them, in order:

  31. Summation Notation In general for a sample of n points of data we call them, in order: When we wish to sum (add them up), we use the notation: This is called summation notation.

  32. Example

  33. Example This says to add up the xi changingi from: 1 to 5

  34. Example

  35. Example

  36. Example

  37. Example

  38. Example

  39. Example

  40. Example

  41. Example

  42. Example

  43. Example

  44. Example

  45. Example

  46. Example

  47. Example

  48. Summation Notation In statistics, sometimes the i is not included in the sum since it is implied that we are summing over all points in our data set. That is you may see the following:

  49. Descriptive Statistics • Qualitative Variables • Graphical Methods • Quantitative Variables • Graphical Methods

  50. Descriptive Statistics • Qualitative Variables • Graphical Methods • Quantitative Variables • Graphical Methods • Numerical Methods

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