Sample annual salaries? (in thousands of? dollars) for employees at a company are listed. 50 50??...

Sample annual salaries? (in thousands of? dollars) for employees at a company are listed. 50 50?? 47 47?? 59 59?? 54 54?? 28 28?? 28 28?? 50 50?? 47 47?? 59 59?? 27 27?? 54 54?? 50 50?? 45 45 ?(a) Find the sample mean and sample standard deviation. ?(b) Each employee in the sample is given a 5 5?% raise. Find the sample mean and sample standard deviation for the revised data set. ?(c) To calculate the monthly? salary, divide each original salary by 12. Find the sample mean and sample standard deviation for the revised data set. ?(d) What can you conclude from the results of? (a), (b), and? (c)? ?(a) The sample mean is x overbar x equals = nothing thousand dollars. ?(Round to one decimal place as? needed.)

Expert Solution

a) mean() = (50 + 47 + 59 + 54 + 28 + 28 + 50 + 47 + 59 + 27 + 54 + 50 + 45)/13 = 46

standard deviation(s) = sqrt(((50 - 46)^2 + (47 - 46)^2 + (59 - 46)^2 + (54 - 46)^2 + (28 - 46)^2 + (28 - 46)^2 + (50 - 46)^2 + (47 - 46)^2 + (59 - 46)^2 + (27 - 46)^2 + (54 - 46)^2 + (50 - 46)^2 + (45 - 46)^2)/13) = 10.8

b) After raising 5% the new samples will be

52.5, 49.35, 61.95, 56.7, 29.4, 29.4, 52.5, 49.35, 61.95, 28.35, 56.7, 52.5, 47.25

mean() = (52.5 + 49.35 + 61.95 + 56.7 + 29.4 + 29.4 + 52.5 + 49.35 + 61.95 + 28.35 + 56.7 + 52.5 + 47.25)/13

= 48.3

standard deviation(s) = sqrt(((52.5 - 48.3)^2 + (49.35 - 48.3)^2 + (61.95 - 48.3)^2 + (56.7 - 48.3)^2 + (29.4 - 48.3)^2 + (29.4 - 48.3)^2 + (52.5 - 48.3)^2 + (49.35 - 48.3)^2 + (61.95 - 48.3)^2 + (28.35 - 48.3)^2 + (56.7 - 48.3)^2 + (52.5 - 48.3)^2 + (47.25 - 48.3)^2)/13) = 11.4

c) By dividing original salary by 12, the new sample will be

4.17, 3.92, 4.92, 4.5, 2.33, 2.33, 4.17, 3.92, 4.92, 2.25, 4.5, 4.17, 3.75

mean() = (4.17 + 3.92 + 4.92 + 4.5 + 2.33 + 2.33 + 4.17 + 3.92 + 4.92 + 2.25 + 4.5 + 4.17 + 3.75)/13

= 3.8

standard deviation(s) = sqrt(((4.17 - 3.8)^2 + (3.92 - 3.8)^2 + (4.92 - 3.8)^2 + (4.5 - 3.8)^2 + (2.33 - 3.8)^2 + (2.33 - 3.8)^2 + (4.17 - 3.8)^2 + (3.92 - 3.8)^2 + (4.92 - 3.8)^2 + (2.25 - 3.8)^2 + (4.5 - 3.8)^2 + (4.17 - 3.8)^2 + (3.75 - 3.8)^2)/13) = 0.9

orchestra answered 2 years ago

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