92 CHAPTER 3 Describing, Exploring, and Comparing Data ■ When more than two data values occur with the same greatest frequency, each is a mode, and the data set is said to be multimodal. ■ When no data value is repeated, we say that there is no mode. ■ When you have ice cream with your pie, it is “à la mode.” Two modes: The wait times (mins) of 30, 30, 50, 50, and 75 have two modes: 30 mins and 50 mins. No mode: The wait times (mins) of 20, 30, 35, 50, and 75 have no mode because no value is repeated. Midrange Another measure of center is the midrange. DEFINITION The midrange of a data set is the measure of center that is the value midway between the maximum and minimum values in the original data set. It is found by adding the maximum data value to the minimum data value and then dividing the sum by 2, as in the following formula: Midrange = maximum data value + minimum data value 2 Important Properties of the Midrange ■ Because the midrange uses only the maximum and minimum values, it is very sensitive to those extremes so the midrange is not resistant. ■ In practice, the midrange is rarely used, but it has three redeeming features: 1. The midrange is very easy to compute. 2. The midrange helps reinforce the very important point that there are several different ways to define the center of a data set. 3. The value of the midrange is sometimes used incorrectly for the median, so confusion can be reduced by clearly defining the midrange along with the median. In Example 4, the mode is a single value. Here are other possible circumstances: The Changing Average American According to The New York Times, the average American man weighs 198 pounds, is 69 inches tall, and has a 40-inch waist. The average American woman weighs 171 pounds, is 64 inches tall, and has a 39-inch waist. Since 1960, men have gained an average of 32 pounds and women gained an average of 31 pounds. It’s extremely important to stay current with such averages, because they affect our safety and comfort when designing airplanes, elevators, boats, and many other devices. Accurate data collection is always important, and CDC epidemiologist Cynthia Ogden notes that “people tend to overreport their height and underreport their weight.” Thankfully, the preceding averages are based on actual physical measurements instead of relying on measurements reported by the study subjects. A A CP EXAMPLE 4 Mode Find the mode of the first eleven wait times for “Tower of Terror” at 10 AM. 35 35 20 50 95 75 45 50 30 35 30 SOLUTION Sort the list to make it easier to find values that occur more than once: 20 30 30 35 35 35 45 50 50 75 95 The mode is 35 minutes, because it is the value occurring most often (three times). YOUR TURN. Find the mode in Exercise 7 “Celebrity Net Worth.”
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