Measuring Variation – Boxplots

1. Measuring Variation – Boxplots Lecture 19 Sec. 5.3.3 Tue, Feb 20, 2007

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, 175, 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 Med 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 WINDOW. • Set minX and maxX appropriately. • Or press ZOOM. • Select ZoomStat (#9) and press ENTER. • Press GRAPH.

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. Example • Draw a modified boxplot of the sample 9, 12, 39, 40, 42, 46, 49, 54, 58, 60, 84.

21. TI-83 – Modified Boxplots • Follow the same steps as for a regular boxplot, but for the Type, select the modified-boxplot icon, the first icon in the second row. • It looks like a boxplot with a couple of extra dots. • Use the TI-83 to find a modified boxplot of the sample data 9, 12, 39, 40, 42, 46, 49, 54, 58, 75, 84.

22. Example: DePaul University • For an example of modified boxplots, see DePaul University’s web page on retention.