Question

(a) each employee ... revised data set.
(c) to calculate the monthly salary, divide each original salary by 12 deviation for the revised data set.
(d) what can you conclude from the results of (a), (b), and (c)?
(round to one decimal place as needed.)
the sample standard deviation is s = 10.3 thousand dollars.
(round to one decimal place as needed.)
(b) the sample mean is \\( \bar{x} = 47.2 \\) thousand dollars.
(round to one decimal place as needed.)
the sample standard deviation is s = 10.3 thousand dollars.
(round to one decimal place as needed.)
(c) the sample mean is \\( \bar{x} = \square \\) thousand dollars.
(round to one decimal place as needed.)

Explanation:

Step1: Recall the property of the mean

When each data point \( x_i \) is divided by a constant \( c \) (here \( c = 12 \) to get monthly salary from annual salary), the new mean \( \bar{x}_{new} \) is related to the old mean \( \bar{x}_{old} \) by the formula \( \bar{x}_{new}=\frac{\bar{x}_{old}}{c} \).

Step2: Use the given old mean

From part (b), the sample mean of the annual salaries (old mean) is \( \bar{x}_{old} = 47.2 \) thousand dollars. We need to find the mean of the monthly salaries, so we divide the old mean by 12.

\[
\bar{x}_{new}=\frac{47.2}{12} \approx 3.9
\]

Answer:

\( 3.9 \)