3-1 Measures of Center 95 Well, how can that be? The wait times for both rides have the same measures of center! Instead of being a phenomenon that commonly occurs, the wait times from Figure 3-2 have been carefully selected. Because the wait times for the two different rides have the same measures of center, they appear to be behaving the same, but this is really, really important: Go back and examine the two sets of wait times in Figure 3-2 and try to identify a fundamental and dramatic difference that is not identified by the measures of center. Find it? If not, SPOILER ALERT: Section 3-2 identifies and investigates this important difference. (See Example 8 on page 114.) PART 2 Beyond the Basics of Measures of Center Calculating the Mean from a Frequency Distribution Formula 3-2 is the same calculation for the mean that was presented in Part 1, but it incorporates this approach: When working with data summarized in a frequency distribution, we make calculations possible by pretending that all sample values in each class are equal to the class midpoint. Formula 3-2 is not really a new concept; it is simply a variation of Formula 3-1 (mean). TABLE 3-2 Comparison of Disney Wait Times (minutes) Mean Median Mode Midrange Rock ‘n’ Roller Coaster 57.3 55.0 45 62.5 Tower of Terror 57.3 55.0 45 62.5 Example 7 illustrates the procedure for finding the mean from a frequency distribution. FORMULA 3-2 MEAN FROM A FREQUENCY DISTRIBUTION First multiply each frequency and class midpoint; then add the products. T x = Σ1f # x2 Σf 1Result is an approximation2 c Sum of frequencies 1equal to n2 TABLE 3-3 Daily Commute Time in Los Angeles Daily Commute Times in Los Angeles (minutes) Frequency ƒ Class Midpoint x ƒ # x 0–14 6 7.0 42.0 15–29 18 22.0 396.0 30–44 14 37.0 518.0 45–59 5 52.0 260.0 60–74 5 67.0 335.0 75–89 1 82.0 82.0 90–104 1 97.0 97.0 Totals: aƒ = 50 a1ƒ# x2 = 1730.0 continued Go Figure 1: The mean number of hours Americans spend daily looking for something. EXAMPLE 7 Computing the Mean from a Frequency Distribution The first two columns of Table 3-3 shown here are the same as the Los Angeles commute time frequency distribution of Table 2-2 from Chapter 2. Use the frequency distribution in the first two columns of Table 3-3 to find the mean.
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