91Ó°ÊÓ

To find the mean, add the numbers and then divide by the number of values in the data set.

$\begin{array}{l}\stackrel{¯}{x}=\frac{4+5+5+6+6+8+9+10}{8}\\ =\frac{53}{8}\\ =6.625\end{array}$

To find the variance, square the difference between each number and the mean. Then add the squares, and divide by the number of values.

$\begin{array}{l}{\mathrm{σ}}^2=\frac{{(4−6.63)}^2+{(5−6.63)}^2+{(5−6.63)}^2+{(6−6.63)}^2+{(6−6.63)}^2+{(8−6.63)}^2+{(9−6.63)}^2+{(10−6.63)}^2}{8}\\ =\frac{{(−2.625)}^2+{(−1.625)}^2+{(−1.625)}^2+{(−0.625)}^2+{(−0.625)}^2+{\left(1.375\right)}^2+{\left(2.375\right)}^2+{\left(3.375\right)}^2}{8}\\ =\frac{6.890625+2.640625+2.640625+0.390625+0.390625+1.890625+5.640625+11.390625}{8}\\ =\frac{31.875}{8}\\ =3.984\end{array}$

To find the standard deviation, take square root of the variance.

$\begin{array}{c}{\mathrm{σ}}^2=3.984\\ \mathrm{σ}=\sqrt{3.984}\\ =1.996≈2\end{array}$

Therefore, the mean, variance and standard variation of the given data set is$6.625,3.984$ and 2 respectively.