Cumulative Review 127 In Exercises 11 and 12, determine whether the data are qualitative or quantitative, and determine the level of measurement of the data set. 11. The amounts of time (in months) that 16 stars of The Bachelorette and their chosen partner stayed together as of April 2021 are listed. 208 12 3 12 18 94 3 75 8 36 75 20 24 0 4 5 12. The six top-earning states in 2019 by median household income are listed. (Source: U.S. Census Bureau) 1. Maryland 2. New Jersey 3. Hawaii 4. Massachusetts 5. Connecticut 6. Alaska 13. The number of tornadoes by state in 2020 are listed. (a) Draw a box-and-whisker plot that represents the data set and (b) describe the shape of the distribution. (Source: National Oceanic and Atmospheric Administration) 78 0 4 41 7 34 6 7 65 75 0 0 71 18 28 27 23 55 2 21 3 2 69 127 27 2 35 0 2 5 6 10 54 22 19 31 3 6 0 57 21 38 102 0 0 15 2 0 22 1 14. Five test scores are shown below. The first 4 test scores are 15% of the final grade, and the last test score is 40% of the final grade. Find the weighted mean of the test scores. 85 92 84 89 91 15. Tail lengths (in feet) for a sample of American alligators are listed. 6.5 3.4 4.2 7.1 5.4 6.8 7.5 3.9 4.6 (a) Find the mean, median, and mode of the tail lengths. Which best describes a typical American alligator tail length? Explain your reasoning. (b) Find the range, variance, and standard deviation of the data set. 16. A study shows that life expectancies for Americans have increased or remained stable every year for the past five years. (a) Make an inference based on the results of the study. (b) What is wrong with this type of reasoning? In Exercises 17–19, use the data set, which represents the points recorded by each player on the Winnipeg Jets in the 2019–2020 NHL season. (Source: National Hockey League) 8 8 8 6 0 73 26 1 0 5 58 1 7 5 10 63 0 5 10 0 31 5 15 45 16 29 10 73 5 3 0 65 17. Construct a frequency distribution for the data set using eight classes. Include class limits, midpoints, boundaries, frequencies, relative frequencies, and cumulative frequencies. 18. Describe the shape of the distribution. 19. Construct a relative frequency histogram using the frequency distribution in Exercise 17. Then determine which class has the greatest relative frequency and which has the least relative frequency.
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