3-3 Measures of Relative Standing and Boxplots 131 CAUTION Because there is not universal agreement on procedures for finding quartiles, and because modified boxplots are based on quartiles, different technologies may yield different modified boxplots. CP EXAMPLE 9 Constructing a Modified Boxplot Use the fifty “Space Mountain” 10 AM wait times in Table 3-6 on page 124 (Data Set 33 “Disney World Wait Times” in Appendix B) to construct a modified boxplot. SOLUTION Let’s begin with the above four steps for identifying outliers in a modified boxplot. 1. Using the “Space Mountain” wait times, the three quartiles are Q1 = 25, the median is Q2 = 35, and Q3 = 50. (All values are in minutes, and these quartiles were found in Example 6.) 2. The interquartile range is IQR = Q3 - Q1 = 50 - 25 = 25. 3. 1.5 * IQR = 1.5 * 25 = 37.5 4. Any outliers are above Q3 = 50 by more than 37.5, or below Q1 = 25 by more than 37.5. This means that any outliers are greater than 87.5, or less than -12.5 (which is impossible, so there can be no outliers at the low end in this example). We can now examine the original “Space Mountain” wait times to identify any wait times greater than 87.5, and we find these values: 105 and 110. The only outliers are 105 and 110. We can now construct the modified boxplot shown in Figure 3-11. In Figure 3-11, the two outliers are identified as special points, the three quartiles are shown as in a regular boxplot, and the horizontal line extends from the lowest data value that is not an outlier 1102 to the highest data value that is not an outlier 1752. FIGURE 3-11 Modified Boxplot of “Space Mountain” 10 AM Wait Times YOUR TURN. Do Exercise 37 “Outliers and Modified Boxplots.”
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