3-1 Measures of Center 99 from lowest to highest. Find the mean and median of these ten values. Then find the mean and median after excluding the value of 180, which appears to be an outlier. Compare the two sets of results. How much was the mean affected by the inclusion of the outlier? How much is the median affected by the inclusion of the outlier? 15 20 25 30 30 35 45 50 50 180 Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question. 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. Find the mean and median. 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). Find the mean and median. 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 in the year 1984. 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 measures of center? Based on these data, would the college have been justified by saying that the mean income of a graduate in their geography program is greater than $250,000? 17,466 18,085 17,875 19,339 19,682 19,610 18,259 16,354 2,200,000 9. Jaws 2 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 center? 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 center 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. If you decide to buy one of these smart thermostats, what statistic is most relevant, other than the measures of central tendency? 250 170 225 100 250 250 130 200 150 250 170 200 180 250 12. Cell Phone Radiation Listed below are the measured radiation levels (in W/kg) corresponding to these cell phones: iPhone X, iPhone 7, Google Pixel, Samsung Galaxy S8, OnePlus 5, Motorola VE465, LG G3, and HTC Desire 310. The data are from the Federal Communications Commission. The media often report about the dangers of cell phone radiation as
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