[tex]10.68[/tex]
1) Let's write this dataset in ascending order:
[tex]42,52,58,63,70[/tex]
2) Now, let's calculate the standard deviation from the mean of that sample:
[tex]s\left(x\right)=\sqrt{\frac{\sum_{i=1}^n\left(x_i-\bar{x}\right)^2}{n-1}}[/tex]
But before that, let's find the mean and the variance:
[tex]\begin{gathered} \\ \bar{x}=\frac{1}{n}\sum_{i=1}^na_i=\frac{285}{5}=57 \\ \\ Var\left(X\right)=\sum_{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1}= \\ \\ \frac{\left(42-57\right)^2+\left(52-57\right)^2+\left(58-57\right)^2+\left(63-57\right)^2+\left(70-57\right)^2}{5-1} \\ \\ Var\left(X\right)=\frac{456}{4}=114 \\ \\ \end{gathered}[/tex]
3) Finally, we can take the square root of the variance:
[tex]s(x)=\sqrt{\sum_{i=1}^n\frac{\left(x_i-\bar{x}\right)^2}{n-1}}=\sqrt{\frac{114}{4}}=10.67707\approx10.68[/tex]
