128 CHAPTER 3 Describing, Exploring, and Comparing Data CAUTION Because there is not universal agreement on procedures for finding quartiles, and because boxplots are based on quartiles, different technologies may yield different boxplots. CP EXAMPLE 7 Constructing a Boxplot Use the “Space Mountain” wait times listed in Table 3-6 to construct a boxplot. SOLUTION The boxplot uses the 5-number summary found in Example 6: 10, 25, 35, 50, and 110 (all in minutes). Figure 3-8 is the boxplot representing the “Space Mountain” wait times listed in Table 3-6. FIGURE 3-8 Boxplot of “Space Mountain” Wait Times (minutes) YOUR TURN. Construct the boxplot in Exercise 31 “Radiation in Baby Teeth.” Skewness A boxplot can often be used to identify skewness. Recall that in Section 2-2 we stated that a distribution of data is skewed if it is not symmetric and extends more to one side than to the other. In a histogram of data skewed to the right (also called positively skewed), there is a longer right tail showing that relatively few data values are high data values; most of the data values are located at the left. The boxplot in Figure 3-8 shows that the data are skewed to the right, and most of the data values are located at the left. Because the shape of a boxplot is determined by the five values from the 5-number summary, a boxplot is not a graph of the distribution of the data, and it doesn’t show as much detailed information as a histogram or stemplot. However, boxplots are often great for comparing two or more data sets. When using two or more boxplots for comparing different data sets, graph the boxplots on the same scale so that comparisons can be easily made. Methods discussed later in this book allow us to analyze comparisons of data sets more formally than subjective conclusions based on a graph. It is always wise to construct suitable graphs, such as histograms, dotplots, and boxplots, but we should not rely solely on subjective judgments based on graphs. EXAMPLE 8 Comparing the Wait Times at Popular Walt Disney World Rides Data Set 33 “Disney World Wait Times” includes wait times for several popular rides at 10 AM on fifty different days. Use the same scale to construct the boxplots for “Space Mountain,” “Tower of Terror,” and “Avatar Flight of Passage”; then compare the results. SOLUTION The Statdisk-generated boxplots shown in Figure 3-9 suggest that “Avatar Flight of Passage” has the longest wait time, and that “Space Mountain” and “Tower of Terror” wait times are similar to each other in both their measures of center and variation. CP
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