Question

sample annual salaries (in thousands of dollars) for employees at a company are listed
50 44 53 47 39 39 50 44 53 32 47 50 48
(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 the 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 \\( \overline { x } = \\) thousand dollars.
(round to one decimal place as needed.)

Explanation:

Step1: Count the number of data points

There are \(n = 13\) data points: \(50,44,53,47,39,39,50,44,53,32,47,50,48\)

Step2: Calculate the sum of the data points

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Step3: Calculate the sample mean

The formula for the sample mean \(\bar{x}=\frac{\sum x}{n}\). Substitute \(\sum x = 596\) and \(n = 13\)

$$ \bar{x}=\frac{596}{13}\approx45.8 $$

Answer:

\(45.8\)