124 CHAPTER 3 Describing, Exploring, and Comparing Data CP TABLE 3-6 Sorted “Space Mountain” 10 AM Wait Times 10 15 15 15 15 15 20 20 20 20 25 25 25 25 25 25 30 30 30 30 30 30 30 30 35 35 35 35 35 35 35 35 40 40 40 40 45 50 50 50 50 50 55 55 60 75 75 75 105 110 EXAMPLE 3 Finding a Percentile Table 3-6 lists the fifty “Space Mountain” 10 AM wait times from Data Set 33 “Disney World Wait Times.” These wait times are arranged in increasing order in Table 3-6. Find the percentile for the wait time of 45 minutes. SOLUTION From the sorted list of wait times in Table 3-6, we see that there are 36 wait times less than 45 minutes, so Percentile of 45 = 36 50 # 100 = 72 INTERPRETATION A wait time of 45 minutes is in the 72nd percentile. This can be interpreted loosely as this: A wait time of 45 minutes separates the lowest 72% of values from the highest 28% of values. We have P72 = 45 minutes. YOUR TURN. Do Exercise 17 “Percentiles.” Example 3 shows how to convert from a given sample value to the corresponding percentile. There are several different methods for the reverse procedure of converting a given percentile to the corresponding value in the data set. The procedure we will use is summarized in Figure 3-7, which uses the following notation. Notation n total number of values in the data set k percentile being used (Example: For the 25th percentile, k = 25.) L locator that gives the position of a value (Example: For the 12th value in the sorted list, L = 12.) Pk kth percentile (Example: P25 is the 25th percentile.) The 50th percentile, denoted P50, has about 50% of the data values below it and about 50% of the data values above it, so the 50th percentile is the same as the median. There is not universal agreement on a single procedure for calculating percentiles, but we will describe relatively simple procedures for (1) finding the percentile of a data value and (2) converting a percentile to its corresponding data value. We begin with the first procedure. Finding the Percentile of a Data Value The process of finding the percentile that corresponds to a particular data value x is given by the following (round the result to the nearest whole number): Percentile of value x = number of values less than x total number of values # 100 T 5 T w Go Figure 640K: The amount of computer memory that in 1981 Microsoft founder Bill Gates allegedly thought would be “enough for anybody.” Bill Gates: “I’ve said some stupid things and some wrong things, but not that.”
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