The variance of a given data set with size N is given by the formula:
[tex]\begin{gathered} \sigma=\sqrt{\frac{1}{N}\sum_{i=1}^N(x_i-\mu)^2} \\ Var(X)=\sigma^2 \end{gathered}[/tex]Then, for the data set {22, 26, 17, 20, 20} and N = 5, we have:
[tex]\begin{gathered} \mu=\frac{22+26+17+20+20}{5}=21 \\ \sigma=\sqrt{\frac{1^2+5^2+(-4)^2+(-1)^2+(-1)^2}{5}}=\sqrt{\frac{44}{5}}=2\sqrt{\frac{11}{5}} \\ \therefore Var(X)=\frac{44}{5}=8.8 \end{gathered}[/tex]