3-3 Measures of Relative Standing and Boxplots 125 The value of Pk is the Lth value, counting from the lowest. Is L a whole number? Yes No Change L by rounding it up to the next larger whole number. Compute n 5 number of values k 5 percentile in question Sort the data. (Arrange the data in order of lowest to highest.) Start L 5 n where k 100 The value of the kth percentile is midway between the Lth value and the next value in the sorted set of data. Find Pk by adding the Lth value and the next value and dividing the total by 2. FIGURE 3-7 Converting from the kth percentile to the corresponding data value CP EXAMPLE 4 Converting a Percentile to a Data Value Refer to the fifty sorted “Space Mountain” wait times in Table 3-6 and use the procedure in Figure 3-7 to find the value of the 25th percentile, P25. SOLUTION From Figure 3-7, we see that the sample data are already sorted, so we can proceed to find the value of the locator L. In this computation we use k = 25 because we are trying to find the value of the 25th percentile. We use n = 50 because there are 50 data values. L = k 100 # n = 25 100 # 50 = 12.5 Since L = 12.5 is not a whole number, we proceed to the next lower box in Figure 3-7, where we change L by rounding it up from 12.5 to the next larger whole number: 13. (In this book we typically round off the usual way, but this is one of two cases where we round up instead of rounding off.) From the bottom box we see that the value of P25 is the 13th value, counting from the lowest. In Table 3-6, the 13th value is 25. That is, P25 = 25 minutes. Roughly speaking, about 25% of the wait times are less than 25 minutes and 75% of the wait times are more than 25 minutes. YOUR TURN. Do Exercise 27 “Percentile.”
RkJQdWJsaXNoZXIy NjM5ODQ=