128 Chapter 3 Numerical Summaries of Data Step 1: The sorted data are presented in Table 3.10. Step 2: There are n = 42 rainfall values in the data set. For the first quartile, we follow the procedure for computing the 25th percentile. We first compute L = 25 100 × 42 = 10.5 Step 3: Since L = 10.5 is a not whole number, we round it up to 11. The first quartile, Q1, is the number in the 11th position. From Table 3.10, we see that this number is 0.67. So Q1 = 0.67. Step 4: For the third quartile, we compute L = 75 100 × 42 = 31.5 Step 5: Since 31.5 is not a whole number, we round it up to 32. The third quartile, Q3, is the value in the 32nd position. From Table 3.10, we see that Q3 = 5.54. Figure 3.8 presents a dotplot of the Los Angeles rainfall data set with the quartiles indicated. The quartiles divide the data set into four parts, with approximately 25% of the data in each part. Recall that the median is the same as the second quartile. Since there are 42 values in this data set, the median is the average of the 21st and 22nd values when the data are arranged in order. From Table 3.10, we can see that the median is 2.95. 0 2 4 6 8 10 12 14 First quartile Median Largest data value 25% of the data 25% of the data 25% of the data 25% of the data Smallest data value Third quartile Figure 3.8 The quartiles of the Los Angeles rainfall data set EXAMPLE 3.26 Using technology to compute quartiles Use technology to compute the first and third quartiles for the Los Angeles rainfall data, presented in Table 3.9. Solution Figure 3.9 presents MINITAB output. The quartiles are highlighted in red. Note that the values produced by MINITAB differ slightly from the results obtained in Example 3.25, because MINITAB uses a slightly different procedure than the one we describe here. The MINITAB procedure for computing the mean and median will also compute the quartiles. Step-by-step instructions are presented in the Using Technology section on page 96. Variable N Mean SE Mean StDev Minimum Q1 Median Q3 Maximum Rainfall 42 3.749 0.559 3.624 0.000 0.643 2.950 5.680 13.680 Figure 3.9
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