116 CHAPTER 3 Describing, Exploring, and Comparing Data 2. Range Rule of Thumb for Interpreting s The 153 heights of males from Data Set 1 “Body Data” in Appendix B have a mean of 174.12 cm and a standard deviation of 7.10 cm. Use the range rule of thumb to identify the limits separating values that are significantly low or significantly high. For such data, would a height of 190 cm be significantly high? 3. Variance The 153 heights of males from Data Set 1 “Body Data” in Appendix B have a standard deviation of 7.10 cm. What is the variance of their heights? Be sure to include the appropriate units with the result. 4. Symbols Identify the symbols used for each of the following: (a) sample standard deviation; (b) population standard deviation; (c) sample variance; (d) population variance. If sample data consist of weights measured in grams, what units are used for these statistics and parameters? In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions. 5. Super Bowl Jersey Numbers Listed below are the jersey numbers of the 11 offensive players on the starting roster of the New England Patriots when they won Super Bowl LIII. What do the results tell us? 12 26 46 15 11 87 77 62 60 69 61 6. Super Bowl Ages Listed below are the ages of the same 11 players used in the preceding exercise. How are the resulting statistics fundamentally different from those found in the preceding exercise? 41 24 30 31 32 29 25 26 26 25 30 7. Celebrity Net Worth Here are the celebrities with the top 8 net worths (in millions of dollars) in a recent year: George Lucas (5500), Steven Spielberg (3700), Oprah Winfrey (3200), Michael Jordan (1700), Paul McCartney (1200), J. K. Rowling (1000), David Copperfield (1000), and Jerry Seinfeld (950). What do the results tell us about the population of all celebrities? Based on the nature of the amounts, what can be inferred about their precision? 8. Geography Majors The data listed below are estimated incomes (dollars) of students who graduated from the University of North Carolina (UNC) after majoring in geography. The data are based on graduates from the year 1984, and the income of basketball superstar Michael Jordan (a 1984 UNC graduate and geography major) is included. Does his income have much of an effect on the results? 17,466 18,085 17,875 19,339 19,682 19,610 18,259 16,354 2,200,000 9. Jaws 3 Listed below are the number of unprovoked shark attacks worldwide for the last several years. What extremely important characteristic of the data is not considered when finding the measures of variation? 70 54 68 82 79 83 76 73 98 81 10. Peas in a Pod Biologists conducted experiments to determine whether a deficiency of carbon dioxide in the soil affects the phenotypes of peas. Listed below are the phenotype codes, where 1 = smooth@yellow, 2 = smooth@green, 3 = wrinkled@yellow, and 4 = wrinkled@green. Can the measures of variation be obtained for these values? Do the results make sense? 2 1 1 1 1 1 1 4 1 2 2 1 2 3 3 2 3 1 3 1 3 1 3 2 2 11. Smart Thermostats Listed below are selling prices (dollars) of smart thermostats tested by Consumer Reports magazine. Are any of the resulting statistics helpful in selecting a smart thermostat for purchase? 250 170 225 100 250 250 130 200 150 250 170 200 180 250 12. Cell Phone Radiation Listed below are the measured radiation rates (in W>kg) corresponding to these cell phones: iPhone X, iPhone 7, Google Pixel, Samsung Galaxy S8, OnePlus 5,
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