98 CHAPTER 2 Descriptive Statistics Comparing Variation in Different Data Sets In Exercises 45–50, find the coefficient of variation for each of the two data sets. Then compare the results. 45. Annual Salaries Sample annual salaries (in thousands of dollars) for entry level architects in Denver, CO, and Los Angeles, CA, are listed. Denver 55.2 55.8 53.8 50.1 60.9 48.9 53.6 62.5 54.2 61.0 50.7 58.4 Los Angeles 68.4 62.3 67.7 60.2 67.4 67.3 59.3 68.0 59.8 58.0 63.6 72.9 46. Annual Salaries Sample annual salaries (in thousands of dollars) for entry level software engineers in Raleigh, NC, and Wichita, KS, are listed. Raleigh 69.5 74.2 65.1 56.5 65.6 62.1 79.5 72.4 58.3 Wichita 59.7 76.0 57.1 79.7 55.2 70.7 80.0 78.8 64.2 47. Ages and Caps The ages (in years) and caps (number of matches played) of all members of the 2021 Women’s U.S. soccer team are listed. (Source: U.S. Soccer) Ages 26 23 27 22 28 28 26 25 38 21 30 28 31 24 32 32 32 25 35 35 20 27 27 Caps 5 2 65 28 109 108 91 51 299 3 21 70 173 0 67 134 142 6 173 182 3 51 33 48. Heights and Weights The heights (in inches) and weights (in pounds) of every France national soccer team player that started the 2018 FIFA Men’s World Cup final are listed. (Source: ESPN) Heights 74 73 75 72 72 76 66 70 69 69 76 Weights 181 168 179 163 168 183 150 161 161 152 203 49. SAT Scores Sample SAT scores for eight males and eight females are listed. Males 1010 1170 1410 920 1320 1100 690 1140 Females 1190 1010 1000 1300 1470 1250 840 1060 50. Grade Point Averages Sample grade point averages for ten male students and ten female students are listed. Males 2.4 3.7 3.8 3.9 2.8 2.6 3.6 3.3 4.0 1.9 Females 2.8 3.7 2.1 3.9 3.6 4.0 2.0 3.9 3.7 2.3 Extending Concepts 51. Alternative Formula You used SSx = Σ(x - x) 2 when calculating variance and standard deviation. An alternative formula that is sometimes more convenient for hand calculations is SSx = Σx 2 - 1Σx22 n . You can find the sample variance by dividing the sum of squares by n - 1 and the sample standard deviation by finding the square root of the sample variance. (a) Show how to obtain the alternative formula. (b) Use the alternative formula to calculate the sample standard deviation for the data set in Exercise 15. (c) Compare your result with the sample standard deviation obtained in Exercise 15.
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