Answer
Range =$10$
Sample variance = $s^{2}=8$
Sample standard deviation = $s = 2.828$
Work Step by Step
Recall the shortcut formula for calculating the variance ($s^{2}$)$:$
$$s^{2}=\frac{\sum x_{i}^{2}-\frac{(\sum x_{i})^{2}}{n}}{n-1}$$
Create a table in which we compute $\displaystyle \sum x_{i}$ and $\displaystyle \sum x_{i}^{2}$:
$$ \begin{array}{rrr}
& x & x^{2}\\
\hline & 8 & 64\\
& -2 & 4\\
& 1 & 1\\
& 3 & 9\\
& 5 & 25\\
& 4 & 16\\
& 4 & 16\\
& 1 & 1\\
& 3 & 9\\
\hline\rm Sum & 27 & 145
\end{array}$$
Plug in the given values (there are $n=9$ data items):
$$\begin{align*}
s^{2}&= \displaystyle \frac{145-\frac{(27)^{2}}{9}}{9-1} & & \\
& =8 \\\\
s&= \sqrt{8} =2.828 \end{align*}$$
The range is the difference between the largest and smallest data item:
$8-(-2)=10$
