Case Study 85 Case Study: Do Late-Model Cars Get Better Gas Mileage? In the chapter introduction, we presented gas mileage data for 2000 and 2009 model year compact cars. We will use histograms and back-to-back stem-and-leaf plots to compare the mileages between these two groups of cars. The following tables present the mileages, in miles per gallon. Highway Mileage Ratings for 2000 Compact Cars 28 21 30 33 24 29 30 38 27 23 27 34 21 27 38 28 29 21 31 31 32 23 36 28 27 32 31 30 26 23 40 28 27 27 34 28 34 28 38 27 29 27 33 24 31 33 27 28 26 26 31 16 28 30 30 24 37 35 30 33 31 32 Highway Mileage Ratings for 2009 Compact Cars 30 30 27 15 14 17 28 26 25 34 29 26 25 33 35 35 25 30 25 25 25 21 17 18 17 21 18 25 34 33 18 18 27 28 30 25 26 31 30 35 29 29 25 29 28 26 28 26 26 25 30 19 22 26 29 Source: www.fueleconomy.gov 1. Construct a frequency distribution for the 2000 cars with a class width of 1. 2. Explain why a class width of 1 is too narrow for these data. 3. Construct a relative frequency distribution for the 2000 cars with a class width of 2, where the first class has a lower limit of 15. 4. Construct a histogram based on this relative frequency distribution. Is the histogram unimodal or bimodal? Describe the skewness, if any, in these data. 5. Construct a frequency distribution for the 2009 cars with an appropriate class width. 6. Using this class width, construct a relative frequency distribution for the 2009 cars. 7. Construct a histogram based on this relative frequency distribution. Is the histogram unimodal or bimodal? Describe the skewness, if any, in these data. 8. Compare the histogram for the 2000 cars with the histogram for the 2009 cars. Which cars tend to have higher gas mileage? 9. Construct a back-to-back stem-and-leaf plot for these data, using two lines for each stem. Which do you think illustrates the comparison better, the histograms or the back-to-back stem-and-leaf plot? Why?
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