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70 Chapter 1 %u2022 Analyzing One-Variable Data Note that the range of a data set is a single number. In everyday language, people sometimes say things like, %u201cThe data values range from 17 to 308.%u201d Be sure to use the term range correctly, now that you know its statistical definition. caution!A quick trip to school? Finding the range PROBLEM: How long do U.S. high school students typically spend traveling to school? To find out, we recorded the travel times to school (in minutes) for a random sample of 20 U.S. high school students. Here are the data once again, along with a dotplot. 86 Find the range of the distribution. 13 5 4 20 40 7 15 30 5 2 3 8 10 11 15 40 25 5 12 70 25 30 605550454035Travel time to school (min)0 5 10 15 20 65 70SOLUTION: range 7= %u22120 2 =68minutessimonkr/Getty ImagesEXAMPLE FOR PRACTICE TRY EXERCISE 9. range m= aximum %u2013 minimum The range is not a resistant measure of variability. It depends on only the maximum and minimum values, which may be outliers. Look again at the data on travel time to school. Without the possible outlier at 70 minutes, the range of the distribution would decrease to 40 %u2013 2 3 = 8 minutes. The following graph illustrates another problem with using the range as a measure of variability. 87 Many older movies were recorded on high-resolution film with a width of 70 mm, much larger than the standard 35-mm film used for modern movies. The parallel dotplots show the widths (in millimeters) of a sample of 11 strips of 70-mm movie film produced by each of two machines. Both distributions are symmetric, centered at 70 mm, and have a range of 70.2 69. %u2212 = 8 0.4 mm . But the widths of the film strips made by Machine B clearly vary more from the center of 70 mm than the film strips made by Machine A. 69.8 69.9 70.0 70.1 70.2Film strip width (mm)Machine AB The Standard Deviation To avoid the problem illustrated by the film example, we prefer a measure of variability that uses more than just the minimum and maximum values of a quantitative data set. %u00a9 Bedford, Freeman & Worth Publishers. For review purposes only. Do not distribute.