1. Box and Whisker Plot Chapter 3.5

2. Box and Whisker Plot A Box-and-Whisker Plot or Box plot is a visual device that uses a 5-number summary to reveal the characteristics of a data set. It is a graphical display that can be used when there are a small number of data values in a distribution and therefore the construction of a stem-and-leaf display, a bar chart, or a histogram may not be appropriate. It is also useful in identifying whether a distribution’s shape is symmetric or skewed.

3. A General Box and Whisker Plot

4. Box and Whisker on the Calculator Put the data in a list 56, 23, 130, 12, 67, 34, 29, 78, 52, 46 Turn on a Stat Plot (2nd STAT PLOT) with the following settings: Press ZOOM -> 9: ZoomStat -> Enter

5. Press TRACE and the arrow buttons to see the five number summary. Box and Whisker on the Calculator

6. How to Draw a Box and Whisker Plot Steps for Constructing a Box-and-Whisker Plot 1. Draw a horizontal line and scale it from the smallest to the largest data values. (This line is only meant to be a guide.) 2. Draw a rectangular box above the horizontal line with the sides at the 1st quartile, Q1, and the 3rd quartile, Q3. 3. Draw a vertical line within the box to represent the position of the median. 4. Draw horizontal lines from the box to the smallest and largest data values. These are called the Whiskers of the box plot. Min=12 Max = 130 Q1=29Q3=67Med=49 102030405060708090100110120130

7. Interpretation of a Box and Whisker Plot 1. The median represents a measure of the center and is denoted by a vertical line within a rectangular box. 2. Approximately 50% of the data values are contained within the box. 3. Within each component of the box, separated by the median, are approximately 25% of the data values.

8. 4. Approximately the lower 25% of the data values are represented by the whisker connecting the first quartile to the smallest data value. 5.Approximately the upper 25% of the data values are represented by the whisker connecting the third quartile to the largest data value. Interpretation of a Box and Whisker Plot

9. 6. The length of the box is a measure of the variability of the data set. A longer box indicates more variability, while a shorter box will indicate less variability. 7. The length of the whiskers will provide an idea about the shape of the data set. If one whisker is noticeably longer, then the shape of the data set is probably skewed in the direction of the longer whisker. Interpretation of a Box and Whisker Plot

10. Interpretation of the shape of a Box and Whisker Plot

11. Example 3.33 Determine the 5-number summary and draw the Box- and-Whisker plot for the following data 67, 67, 90, 86, 55, 57, 60, 87, 72, 75, 70, 67, 62, 66, 63, 65, 83, 78, 64

12. Example 3.33 5 Number Summary: Min: 55 Q1: 63 Median: 67 Q3: 78 Max: 90 Min=55Max = 90 Q1=63Q3=78 Med=67 50556065707580859095

13. Identifying Outliers Another type of box and whisker plot is called the “modified box and whisker plot.” The modified box and whisker plot will display outliers from a data set.

14. Identifying Outliers Put the data in a list (this is the same data as in the first example) 56, 23, 130, 12, 67, 34, 29, 78, 52, 46 Turn on a Stat Plot (2nd STAT PLOT) with the following settings: Press ZOOM -> 9: ZoomStat -> Enter

15. Identifying Outliers Press TRACE to closely examine the modified Box and Whisker plot. Notice now that the end of the box plot is not the greatest data value. The outlier appears as single dot(s) that can be on either end of the box plot. Here the outlier is 130.