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Displaying Distributions with Graphs - PowerPoint PPT Presentation

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Displaying Distributions with Graphs

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  1. Displaying Distributions with Graphs

  2. Examples:

  3. Examples:

  4. Displaying Distributions with Graphs

  5. Display Shoe Size Human Graph…….. Watch as the graph changes shape. Does the interpretation change also?

  6. Stemplot • Stem (all but the right most digit) • Leaf (the final digit) • Smallest on top to largest on bottom • Leaf in row to right in increasing order • Back-to-back stemplots compare two related distributions: read carefully!!!!!!! • Does not work well for large data sets with each stem holding lots of leaves.

  7. Examples: Stem-and-leaf of Exercise N = 48 Leaf Unit = 100 N* = 5 (30) 0 000000000000000000000011111111 18 0 222233333 9 0 4455 5 0 677 2 0 8 1 1 1 1 1 1 1 1 1 1 1 2 1 2 1 2 1 2 1 2 8

  8. Forty students took a statistics examination having a maximum of 50 points. The score distribution is given in the following stem-and-leaf plot.Stem-and-leaf of Scores on Exam N = 39Leaf Unit = 1.0 2 0 28 6 1 2245 17 2 01333358889(8) 3 00156679 14 4 22444466788 3 5 000

  9. Dotplot • Each observation is a dot above a number line to show the distribution of the variable.

  10. Example:

  11. Histogram • Breaks the range of values into classesand displays only the count or percent of observations in each class. • Always chose classes of equal width. • Five classes is a good minimum but use your best judgment. What you don’t want are gaps (too many classes) or skyscrapers (too few)

  12. Examples:

  13. Five number summary and Boxplots • Minimum: smallest value • Q1: first quartile (25%) • M: median (middle number 50%) second quartile • Q3: third quartile • Maximum: largest value

  14. Examples:

  15. Others • Relative cumulative frequency plot • Time plot

  16. Examples:

  17. Examples:

  18. Calculator Use and Graphs: • Data: Tip of the nose to tip of the finger • 81 95 85 84 87 80 88 97 86 92 89 80 73 85 90 88 82 70 93