ODD ANSWERS A53 17. The data set in (a) has a standard deviation of 2.4 and the data set in (b) has a standard deviation of 5 because the data in (b) have more variability. 19. Company B; An offer of $43,000 is two standard deviations from the mean of Company A’s starting salaries, which makes it unlikely. The same offer is within one standard deviation of the mean of Company B’s starting salaries, which makes the offer likely. 21. (a) Greatest sample standard deviation: (ii) Data set (ii) has more entries that are farther away from the mean. Least sample standard deviation: (iii) Data set (iii) has more entries that are close to the mean. (b) The three data sets have the same mean, median, and mode, but have a different standard deviation. (c) Estimates will vary; (i) s ≈ 1.1; (ii) s ≈ 1.3; (iii) s ≈ 0.8 23. (a) Greatest sample standard deviation: (i) Data set (i) has more entries that are farther away from the mean. Least sample standard deviation: (iii) Data set (iii) has more entries that are close to the mean. (b) The three data sets have the same mean, median, and mode, but have a different standard deviation. (c) Estimates will vary; (i) s ≈ 9.6; (ii) s ≈ 9.0; (iii) s ≈ 5.1 25. Sample answer: 3, 3, 3, 7, 7, 7 27. Sample answer: 9, 9, 9, 9, 9, 9, 9 29. 68% 31. (a) 51 (b) 17 33. 78, 76, and 82 are unusual; 82 is very unusual because it is more than 3 standard deviations from the mean. 35. 30 37. At least 93.75% of the exam scores are from 70 to 94. 39. x f xf 0 3 0 1 4 4 2 3 6 3 9 27 4 3 12 5 3 15 6 8 48 7 5 35 8 6 48 9 6 54 Σ = 50 Σ = 249 x − x 1x − x22 1x − x22f -5 25 75 -4 16 64 -3 9 27 -2 4 36 -1 1 3 0 0 0 1 1 8 2 4 20 3 9 54 4 16 96 Σ = 383 x ≈ 5.0, s ≈ 2.8 41. Class x f xf 17,000 – 19,499 18,249.5 9 155,245.5 19,500–21,999 20,749.5 10 207,495 22,000–24,499 23,249.5 16 371,992 24,500–26,999 25,749.5 11 283,244.5 27,000 or more 28,249.5 6 169,497 n = 52 Σxf = 1,187,474 x − x 1x − x22 1x − x22f -5586.54 31,209,429.17 280,884,862.5 -2086.54 4,353,649.17 43,536,491.72 413.46 170,949.17 2,735,186.75 2913.46 8,488,249.17 93,370,740.89 5413.46 29,305,549.17 175,833,295 Σ1x - x22 f = 596,360,576.9 x ≈ $22,836.04; s ≈ $3419.55 43. x f xf x − x 1x − x22 1x − x22f 1 2 2 -1.9 3.61 7.22 2 18 36 -0.9 0.81 14.58 3 24 72 0.1 0.01 0.24 4 16 64 1.1 1.21 19.36 n = 60 Σxf = 174 Σ1x - x22 f = 41.4 x ≈ 2.9; s ≈ 0.8 45. CVDenver ≈ 8.1%, CVLA ≈ 7.2% Salaries for entry level architects are more variable in Denver than in Los Angeles. 47. CVages ≈ 16.3%, CVcaps ≈ 95.3% Caps are more variable than ages for all members of the 2021 Women’s U.S. soccer team. 49. CVmales ≈ 20.7%, CVfemales ≈ 17.6% SAT scores are more variable for males than for females. 51. (a) SSx = Σ1x - x2 2 SSx = Σ1x 2 - 2xx + x22 SSx = Σx 2 - 2xΣx + x2Σ1 SSx = Σx 2 - 2xΣx + x2n SSx = Σx 2 - 2x2n + x2n SSx = Σx 2 - x2n SSx = Σx 2 - 1Σx22 n (b) s ≈ 1.9 (c) They are the same. 53. (a) x ≈ 42.1; s ≈ 5.6 (b) x ≈ 44.3; s ≈ 5.9 (c) 3.5, 3, 3, 4, 4, 2.75, 4.25, 3.25, 3.25, 3.5, 3.25, 3.75, 3.5, 4.17 x ≈ 3.5; s ≈ 0.47 (d) When each entry is multiplied by a constant k, the new sample mean is k# x, and the new sample standard deviation is k# s.
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