Question

sample annual salaries (in thousands of dollars) for employees at a company are listed.
46 35 45 47 27 27 46 35 45 34 47 46 42
(a) find the sample mean and sample standard deviation.
(b) each employee in the sample is given a $2000 raise. find the sample mean and sample standard deviation for the revised data set.
(c) each employee in the sample takes a pay cut of $2000 from their original salary. 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 \\(\bar{x} = 39.8\\) thousand dollars.
(round to one decimal place as needed.)

Explanation:

Calculate the sample mean

Using the Mean Calculation knowledge point

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Calculate the sample standard deviation

Using the Sample Standard Deviation knowledge point

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Analyze the revised data with a raise

Using the Linear Transformation of Data knowledge point

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Analyze the revised data with a pay cut

Using the Linear Transformation of Data knowledge point

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Formulate the general conclusion

Using the Linear Transformation of Data knowledge point

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Answer:

(a) The sample mean is \(\bar{x} = 39.8\) thousand dollars, and the sample standard deviation is \(s = 8.6\) thousand dollars.

(b) The revised sample mean is \(\bar{x} = 41.8\) thousand dollars, and the sample standard deviation is \(s = 8.6\) thousand dollars.

(c) The revised sample mean is \(\bar{x} = 37.8\) thousand dollars, and the sample standard deviation is \(s = 8.6\) thousand dollars.

(d) Adding or subtracting a constant to each data value in a data set shifts the mean by that constant but leaves the standard deviation unchanged.