Section 3.3 Measures of Position 133 Step 5: The smallest data value that is greater than the lower boundary is 41. We draw a horizontal line from 45 down to 41, as follows: 40 50 60 70 80 90 100 Number of Absences Step 6: We determine, as shown in Example 3.30, that the value 100 is the only outlier. We plot this point separately, to produce the boxplot shown in Figure 3.10. 40 50 60 70 80 90 100 Number of Absences Figure 3.10 Boxplot for the absence data in Table 3.11 Check Your Understanding 4. Construct a boxplot for the payroll data in Table 3.12. Answer is on page 139. Determining the shape of a data set from a boxplot In Section 2.2, we learned howto determine from a histogram whether a data set is symmetric or skewed. In many cases, a boxplot can give us the same information. For example, in the boxplot for the absence data (Figure 3.10), the median is closer to the first quartile than to the third quartile, and the upper whisker is longer than the lower one. This indicates that the data are skewed to the right. Figure 3.11 presents a histogram of the absence data. The skewness is clearly apparent. 35 45 55 65 75 85 95 105 8 6 4 2 0 Frequency Number of Absences Figure 3.11 Histogram for the absence data in Table 3.11 Determining Skewness from a Boxplot • If the median is closer to the first quartile than to the third quartile, or the upper whisker is longer than the lower whisker, the data are skewed to the right. • If the median is closer to the third quartile than to the first quartile, or the lower whisker is longer than the upper whisker, the data are skewed to the left. • If the median is approximately halfway between the first and third quartiles, and the two whiskers are approximately equal in length, the data are approximately symmetric.
navidi_monk_essential_statistics_1e_ch1_3
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