Section 7.6 Assessing Normality 333 Objective 2 Use boxplots to assess normality Boxplots Boxplots are very good for detecting outliers and skewness. They work best for data sets that are not too small. For very small samples, it is just as informative to plot all the points with a dotplot. EXAMPLE 7.31 Using a boxplot to assess normality Recall: Boxplots were introduced in Section 3.3. An insurance adjuster obtains a sample of 20 estimates, in hundreds of dollars, for repairs to cars damaged in collisions. Following are the data. 12.1 15.7 14.2 4.6 8.2 11.6 12.9 11.2 14.9 13.7 6.6 7.2 12.6 9.0 11.9 7.8 9.0 16.2 16.5 12.1 Is it reasonable to treat this as a sample from an approximately normal population? Explain. Solution Figure 7.39 presents a boxplot of the repair estimates. There are no outliers. Although the median is not exactly halfway between the quartiles, the skewness is not great. Therefore, we may treat this as a sample from an approximately normal population. 0 2 4 6 8 10 12 14 16 18 20 Figure 7.39 There are no outliers, and no evidence of strong skewness. Therefore, we may treat this as a sample from an approximately normal population. EXAMPLE 7.32 Using a boxplot to assess normality A recycler determines the amount of recycled newspaper, in cubic feet, collected each week. Following are the results for a sample of 18 weeks. 2129 2853 2530 2054 2075 2011 2162 2285 2668 3194 4834 2469 2380 2567 4117 2337 3179 3157 Is it reasonable to treat this as a sample from an approximately normal population? Explain. Solution Figure 7.40 presents a boxplot of the amount of recycled newspaper. The value 4834 is an outlier. In addition, the upper whisker is much longer than the lower one, which indicates fairly strong skewness. Therefore, we should not treat this as a sample from an approximately normal population. 2000 2500 3000 3500 4000 4500 5000 Figure 7.40 The value 4834 is an outlier, and there is evidence of fairly strong skewness as well. Therefore, we should not treat this as a sample from an approximately normal population. Objective 3 Use histograms to assess normality Histograms Histograms are excellent for detecting strong skewness. They are more effective for data sets that are not too small (for very small data sets, a histogram is just like a dotplot with the dots replaced by rectangles).
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