Section 2.2 Frequency Distributions and Their Graphs 61 c. What are the class limits? d. Construct a frequency histogram. e. Construct a relative frequency distribution. f. Construct a relative frequency histogram. g. What percentage of students play video games less than 10 hours per week? h. What percentage of students play video games 19 or more hours per week? 24. Murder, she wrote: The following frequency distribution presents the number of murders (including negligent manslaughter) per 100,000 population for each U.S. city with population over 250,000 in the year 2008. Murder Rate Frequency 0.0 – 4.9 16 5.0 – 9.9 23 10.0 – 14.9 21 15.0 – 19.9 3 20.0 – 24.9 6 25.0 – 29.9 2 30.0 – 34.9 2 35.0 – 39.9 1 40.0 – 44.9 0 45.0 – 49.9 1 50.0 – 54.9 0 55.0 – 59.9 0 60.0 – 64.9 1 Source: Federal Bureau of Investigation a. How many classes are there? b. What is the class width? c. What are the class limits? d. Construct a frequency histogram. e. Construct a relative frequency distribution. f. Construct a relative frequency histogram. g. What percentage of cities had murder rates less than 20 per 100,000 population? h. What percentage of cities had murder rates of 40 or more per 100,000 population? 25. BMW prices: The following table presents the manufacturer’s suggested retail price (in $1000s) for 2008 base models and styles of BMW automobiles. 28.8 52.0 34.5 49.5 53.8 46.2 50.4 34.9 58.8 36.4 76.6 56.5 54.8 52.4 33.1 54.4 35.6 83.7 64.95 52.5 39.1 32.7 37.4 76.8 83.9 63.0 44.6 34.6 41.2 79.9 100.3 36.7 46.8 39.3 43.0 124.1 106.1 42.7 49.8 41.2 43.5 115.0 38.6 40.7 Source: www.edmunds.com a. Construct a frequency distribution using a class width of 10, and using 20 as the lower class limit for the first class. b. Construct a frequency histogram from the frequency distribution in part (a). c. Construct a relative frequency distribution using the same class width and lower limit for the first class. d. Construct a relative frequency histogram. e. Are the histograms unimodal or bimodal? f. Repeat parts (a)–(d), using a class width of 20, and using 20 as the lower class limit for the first class. g. Do you think that class widths of 10 and 20 are both reasonably good choices for these data, or do you think that one choice is much better than the other? Explain your reasoning. 26. Geysers: The geyser Old Faithful in Yellowstone National Park alternates periods of eruption, which typically last from 1.5 to 4 minutes, with periods of dormancy, which are considerably longer. The following table presents the durations, in minutes, of 60 dormancy periods that occurred during the period January 21–25, 2010. 91 99 99 83 99 85 90 96 88 93 88 88 92 116 59 101 90 71 103 97 82 91 89 89 94 94 61 96 66 105 90 93 88 92 86 93 95 83 90 99 89 94 90 95 93 105 96 92 101 91 94 92 94 86 88 99 90 99 84 92 a. Construct a frequency distribution using a class width of 5, and using 55 as the lower class limit for the first class. b. Construct a frequency histogram from the frequency distribution in part (a). c. Construct a relative frequency distribution using the same class width and lower limit for the first class. d. Construct a relative frequency histogram. e. Are the histograms skewed to the left, skewed to the right, or approximately symmetric? f. Repeat parts (a)–(d), using a class width of 10, and using 50 as the lower class limit for the first class. g. Do you think that class widths of 5 and 10 are both reasonably good choices for these data, or do you think that one choice is much better than the other? Explain your reasoning. 27. Hail to the chief: There have been 56 presidential inaugurations in U.S. history. At each one, the president has made an inaugural address. Following are the number of words spoken in each of these addresses. 1425 135 2308 1729 2158 1175 1209 3217 4467 2906 1125 1172 3838 8445 4776 996 3319 2821 3634 698 1128 1337 2480 2978 1681 4388 2015 3967 2217 985 5433 1802 1526 3318 4059 3801 1883 1807 1340 559 2242 2446 2449 1355 1437 2130 1668 1087 2463 2546 2283 1507 2170 1571 2073 2406 Source: www.infoplease.com a. Construct a frequency distribution with approximately five classes. b. Construct a frequency histogram from the frequency distribution in part (a). c. Construct a relative frequency distribution using the same classes as in part (a). d. Construct a relative frequency histogram from this relative frequency distribution. e. Are the histograms skewed to the left, skewed to the right, or approximately symmetric? f. Construct a frequency distribution with approximately nine classes.
navidi_monk_essential_statistics_1e_ch1_3
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