3-1 Measures of Center 93 CP EXAMPLE 5 Midrange Find the midrange of the first eleven wait times for “Space Mountain” at 10 AM (from Example 1): 50 25 75 35 50 25 30 50 45 25 20 SOLUTION The midrange is found as follows: Midrange = maximum data value + minimum data value 2 = 75 + 20 2 = 47.5 minutes The midrange is 47.5 minutes. YOUR TURN. Find the midrange in Exercise 7 “Celebrity Net Worth.” Round-Off Rules for Measures of Center: • For the mean, median, and midrange, carry one more decimal place than is present in the original set of values. • For the mode, leave the value as is without rounding (because values of the mode are the same as some of the original data values). When applying any rounding rules, round only the final answer, not intermediate values that occur during calculations. See these examples: ■ The mean of 2, 3, and 5 is 3.333333 . . . , which is rounded to 3.3, which has one more decimal place than the original values of 2, 3, and 5. ■ The mean of 80.4 and 80.6 is 80.50 (one more decimal place than was used for the original values). Mode: Because the mode is one or more of the original data values, we do not round values of the mode; we simply use the same original values that are modes. Critical Thinking We can always calculate measures of center from a sample of numbers, but we should always think about whether it makes sense to do that. In Section 1-2 we noted that it makes no sense to do numerical calculations with data at the nominal level of measurement, because those data consist of names, labels, or categories only, so statistics such as the mean and median are meaningless. We should also think about the sampling method used to collect the data. If the sampling method is not sound, the statistics we obtain may be very misleading. Rounding Measures of Center When calculating measures of center, we often need to round the result. We use the following rule. Go Figure Muhammad: The most common first name in the world.
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