Question

sample annual salaries (in thousands of dollars) for employees at a company are listed.
49 42 46 54 40 40 49 42 46 32 54 49 45

(a) find the sample mean and sample standard deviation.
(b) each employee in the sample is given a \\$3000 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 \\$5000 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} = 45.2\\) thousand dollars.
(round to one decimal place as needed.)

the sample standard deviation is \\(s = 6.1\\) thousand dollars.
(round to one decimal place as needed.)

(b) the sample mean is \\(\bar{x} = 48.2\\) thousand dollars.
(round to one decimal place as needed.)

the sample standard deviation is \\(s = \\) thousand dollars.
(round to one decimal place as needed.)

Explanation:

Calculate the original sample mean and standard deviation

Using the Mean Calculation and Sample Standard Deviation knowledge points

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Analyze the effect of adding a constant to each data value

Using the Linear Transformation of Data knowledge point

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Adding a constant to each data value shifts the mean by that constant but leaves the standard deviation unchanged. Therefore, when each employee receives a \$3000 raise (adding 3 to each value in thousands of dollars):

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Answer:

The sample standard deviation is \(s =\) <blank>6.0</blank> thousand dollars.