Calculate the sample standard deviation $s_{n-1}$ for the small sample $\{4,10\}$.

Group A has $n_1=10$ values with a mean ${\mu }_1=60$. Group B has $n_2=40$ values with a mean ${\mu }_2=70$. Calculate the combined mean ${\mu }_{1+2}$ when these two groups are merged.

Calculate the population standard deviation $\sigma$ for the dataset $\{1,3,8\}$. Keep exact values for the mean $\mu$ during the calculation.

A small discrete frequency table is shown below: $$\begin{array}{cc}x& f\\ 0& 1\\ 1& 3\\ 2& 1\end{array}$$ Calculate the population standard deviation $\sigma$ for this data.

Fill in the blank: The standard deviation formula $\sigma =\sqrt{\frac{\sum (x-\mu {)}^2}{n}}$ involves squaring the deviations $(x-\mu )$ primarily to ______.