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Boxplots

Boxplots. Lecture 17 Sec. 5.3.3 Wed, Feb 13, 2008. Boxplots. Boxplot – A graphical display of a five-number summary. Draw and label a scale representing the variable. Draw a box over the scale with its left and right ends at Q1 and Q3. Draw a vertical line through the box at the median.

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Boxplots

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  1. Boxplots Lecture 17 Sec. 5.3.3 Wed, Feb 13, 2008

  2. Boxplots • Boxplot – A graphical display of a five-number summary. • Draw and label a scale representing the variable. • Draw a box over the scale with its left and right ends at Q1 and Q3. • Draw a vertical line through the box at the median. • Draw a left tail (whisker) from the box to the minimum. • Draw a right tail from the box to the maximum.

  3. Example • Draw a boxplot of the sample 5, 20, 30, 45, 60, 80, 100, 140, 150, 200, 240.

  4. Example 0 20 40 60 80 100 120 140 160 180 200 220 240

  5. Example Min Q1 Med Q3 Max 0 20 40 60 80 100 120 140 160 180 200 220 240

  6. Example Min Max 0 20 40 60 80 100 120 140 160 180 200 220 240

  7. Example Min Max 0 20 40 60 80 100 120 140 160 180 200 220 240

  8. Example Max 0 20 40 60 80 100 120 140 160 180 200 220 240

  9. Example 0 20 40 60 80 100 120 140 160 180 200 220 240

  10. Example 0 20 40 60 80 100 120 140 160 180 200 220 240

  11. Boxplots and Shape • What would a boxplot for a uniform distribution look like? • What would a boxplot for a symmetric distribution look like? • What would a boxplot for a right-skewed distribution look like?

  12. TI-83 – Boxplots • Press STAT PLOT. • Select Plot1 • Turn Plot 1 On. • Select the Boxplot Type. • Specify list L1. • Press ZOOM. • Select ZoomStat (#9) and press ENTER.

  13. TI-83 – Boxplots • Press TRACE. • Use the arrow keys to see the values of the minimum, Q1, the median, Q3, and the maximum.

  14. Modified Boxplots • Modified boxplot – A boxplot in which the outliers are indicated.

  15. Modified Boxplots • Draw the box part of the boxplot as usual. • Compute STEP = 1.5  IQR. • The inner fences are at Q1 – STEP and Q3 + STEP. Q1 Q3

  16. Modified Boxplots • Draw the box part of the boxplot as usual. • Compute STEP = 1.5  IQR. • The inner fences are at Q1 – STEP and Q3 + STEP. IQR Q1 Q3

  17. Modified Boxplots • Draw the box part of the boxplot as usual. • Compute STEP = 1.5  IQR. • The inner fences are at Q1 – STEP and Q3 + STEP. 1.5  IQR 1.5  IQR IQR Q1 Q3

  18. Modified Boxplots • Draw the box part of the boxplot as usual. • Compute STEP = 1.5  IQR. • The inner fences are at Q1 – STEP and Q3 + STEP. 1.5  IQR 1.5  IQR IQR Upper fence Lower fence Q1 Q3

  19. Modified Boxplots • Extend the whiskers from the box to the smallest and largest values that are within the inner fences. • Any values that are outside the inner fences should be drawn as individual dots. These dots represent outliers.

  20. Case Study 8 • 2007 Small Arms Study (p. 47) • Find the five-number summary of the data. • Draw a modified boxplot.

  21. Box Plots • For an example of modified boxplots, see DePaul University’s web page on retention.

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