Practice Problems solutions

Practice Problems solutions - Ch. 2, Practice Problems: 11,...

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Ch. 2, Practice Problems: 11, 12, 13, 16, and 21 Ch. 3, Practice Problems: 14, 15, 22, and 25 11 - For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation: 2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0 A. 2, 2, 0, 5, 1, 4, 1, 3, 0, 0, 1, 4, 4, 0, 1, 4, 3, 4, 2, 1, 0 Solution: (a) Mean = sum/21 = 42/21 = 2 (b) Arrange the numbers in ascending order 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 4, 4, 5 Median = middle number = 2 (c) Sum of squared deviations: x x-mean (x-mean)^2 2 0 0 2 0 0 0 -2 4 5 3 9 1 -1 1 4 2 4 1 -1 1 3 1 1 0 -2 4 0 -2 4 1 -1 1 4 2 4 4 2 4 0 -2 4 1 -1 1 4 2 4 3 1 1 4 2 4 2 0 0 1 -1 1 0 -2 4 sum 56 Sum of squared deviation = 56 (d) Variance = Sum of squared deviation/n – 1 = 56/(21 – 1) = 56/20 = 2.8 (e) Standard deviation = √variance = √2.8 = 1.673 12 - For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation: 1,112; 1,245; 1,361; 1,372; 1,472 Solution: (a) Mean = sum/21 = 6562/5 = 1312.4 (b) Arrange the numbers in ascending order 1112, 1,245, 1361, 1372, 1,472 Median = middle number = 1361 (c) Sum of squared deviations: x x-mean (x-mean)^2 1112 -200.4 40160.16 1245 -67.4 4542.76 1361 48.6 2361.96 1372 59.6 3552.16 1472 159.6 25472.16 Sum 76089.2 Sum of squared deviations = 76089.2 (d) Variance = Sum of squared deviation/n – 1 = 76089.2/(5 – 1) = 76089.2/4 = 19022.3 (e) Standard deviation = √variance = √19022.3 = 137.9 13 - For the following scores, find the (a) mean, (b) median, (c) sum of squared deviations, (d) variance, and (e) standard deviation: 3.0, 3.4, 2.6, 3.3, 3.5, 3.2 Solution: (a) Mean = sum/6 = 19/6 = 3.17 (b) Arrange the numbers in ascending order 2.6, 3.0, 3.2, 3.3, 3.4, 3.5 Median = (3.2 + 3.3)/2 = 6.5/2 = 3.25
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(c) Sum of squared deviations: x x-mean (x-mean)^2 3 -0.17 0.0289 3. 4 0.23 0.0529 2.6 -0.57 0.3249 3. 3 0.13 0.0169 3.5 0.33 0.1089 3.2 0.03 0.0009 sum 0.5334 Sum of squared deviations = 0.5334 (d) Variance = Sum of squared deviation/n – 1 = 0.5334/(6 – 1) = 0.5334/5 = 0.1067 (e) Standard deviation = √variance = √0.1067 = 0.3266 16 – A psychologist interested in political behavior measured the square footage of the desks in the official office of four U.S governors and of four chief executive officers (CEOs) of major U.S. corporations. The figures for the governors were 44, 36, 52, and 40 square feet. The figures for the CEOs were 32, 60, 48, 36 square feet. (a) Figure the mean and standard deviation for the governors and for the CEOs. (b) Explain what you have done to a person who has never had a course in statistics. (c) Note that ways in which the means and standard deviations differ, and speculate on the possible meaning of these differences, presuming that they are representative of U.S. governors and large corporations’ CEOs in general.
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Practice Problems solutions - Ch. 2, Practice Problems: 11,...

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