Answer
Range =$3$
Sample variance = $s^{2}=1.3$
Sample standard deviation = $s =1.14$
Work Step by Step
Recall the shortcut formula for calculating the variance ($s^{2}$)$:$
$$s^{2}=\frac{\sum x_{i}^{2}-\frac{(\sum x_{i})^{2}}{n}}{n-1}$$
Let's create a table in which we compute $\displaystyle \sum x_{i}$ and $\displaystyle \sum x_{i}^{2}.$ Recall that we add to all the data items given in the problem text.
$$ \begin{array}{lll}
& x & x^{2}\\
\hline & 5 & 25\\
& 4 & 16\\
& 4 & 16\\
& 3 & 9\\
& 6 & 36\\
\hline\rm Sum & 22 & 102
\end{array}$$
Plug in the given values (there are $n=5$ data items):
$$\begin{align*}
s^{2}&= \displaystyle \frac{102-\frac{(22)^{2}}{5}}{5-1} & & \\
& =1.3 \\\\
s&= \sqrt{1.3} =1.14 \end{align*}$$
The range is the difference between the largest and smallest data item:
$$6-3=3$$
