Question

The monthly salaries (in thousands of dollars) of a sample of 5 sales representatives are as follows.13, 10, 9, 7, 6Send data to calculatorFind the standard deviation of this sample of monthly salaries. Round your answer to two decimal places.(If necessary, consult a list of formulas.)

Answer 1

First, let's calculate the mean of this sample.

The mean is given by the sum of all values divided by the number of values:

$\begin{gathered} \bar{x}=\frac{13+10+9+7+6}{5}\\ \\ \bar{x}=\frac{45}{5}\\ \\ \bar{x}=9 \end{gathered}$

Now, we can use the formula below for the sample standard deviation:

$\begin{gathered} s=\sqrt{\frac{\sum_{i=1}^N(x_i-\bar{x})^2}{N-1}}\\ \\ s=\sqrt{\frac{(13-9)^2+(10-9)^2+(9-9)^2+(7-9)^2+(6-9)^2}{5-1}}\\ \\ s=\sqrt{\frac{16+1+0+4+9}{4}}\\ \\ s=\sqrt{\frac{30}{4}}\\ \\ s=\sqrt{7.5}\\ \\ s=2.74 \end{gathered}$

Therefore the sample standard deviation is 2.74, which represents a salary of $2740.