Question

fill in the blank 1 point
sample annual salaries (in thousands of dollars) for employees at a company are listed.
50 54 55 64 39 39 50 54 55 25 64 50 53
the sample standard deviation is s = type your answer. thousand dollars. round to 1 decimal place.

Explanation:

Step1: Calculate the mean

First, sum all the data values: $50 + 54+55 + 64+39+39+50+54+55+25+64+50+53=653$. There are $n = 13$ data - points. The mean $\bar{x}=\frac{653}{13}\approx50.23$.

Step2: Calculate the squared differences

For each data - point $x_i$, calculate $(x_i-\bar{x})^2$. For example, when $x_1 = 50$, $(50 - 50.23)^2=(-0.23)^2 = 0.0529$. Do this for all 13 data - points and sum them up.
\[

$$\begin{align*} &(50 - 50.23)^2+(54 - 50.23)^2+(55 - 50.23)^2+(64 - 50.23)^2+(39 - 50.23)^2+(39 - 50.23)^2+(50 - 50.23)^2+(54 - 50.23)^2+(55 - 50.23)^2+(25 - 50.23)^2+(64 - 50.23)^2+(50 - 50.23)^2+(53 - 50.23)^2\\ =&0.0529 + 14.2129+22.7529+189.6329+126.1129+126.1129+0.0529+14.2129+22.7529+636.5529+189.6329+0.0529+7.6729\\ =&1349.24 \end{align*}$$

\]

Step3: Calculate the sample variance

The sample variance $s^2=\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}=\frac{1349.24}{13 - 1}=\frac{1349.24}{12}\approx112.44$.

Step4: Calculate the sample standard deviation

The sample standard deviation $s=\sqrt{s^2}=\sqrt{112.44}\approx10.6$.

Answer:

$10.6$