Answer
Sample variance = $s^{2}=0.0587 \text{ ounces}^2$
Sample standard deviation = $s =0.24\text{ ounces}$
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 $\displaystyle \sum x_{i}^{2}.$
$$ \begin{array}{lll}
& x & x^{2}\\
\hline & 0.2 & 0.04\\
& 0.2 & 0.04\\
& 0.2 & 0.04\\
& 0.4 & 0.16\\
& 0.2 & 0.04\\
& 0.8 & 0.64\\
\hline\rm Sum & 2 & 0.96
\end{array}$$
Plug in the given values (there are $n=6$ data items).
$$\begin{align*}
s^{2}&= \displaystyle \frac{0.96-\frac{(2)^{2}}{6}}{6-1} & & \\
& =0.0587 \text{ ounces}^2 \\\\
s&= \sqrt{11.4} =0.24\text{ ounces}
\end{align*} $$
