Solution
First, we calculate the mean.
[tex]\bar{x}=\frac{\sum_^x_i}{n}=\frac{22+28+15+20+20}{5}=21[/tex][tex]\begin{gathered} \sigma^2=\frac{\sum_^(x_i-\bar{x})^2}{n-1} \\ \\ \sigma^2=\frac{\sum_^(x_i-21)^2}{4}=\frac{(22-21)^2+(28-21)^2+(15-21)^2+(20-21)^2+(20-21)^2}{4} \\ \\ \Rightarrow\sigma^2=\frac{1+49+36+1+1}{4}=\frac{88}{4}=22 \end{gathered}[/tex]
Therefore, Variance = 22
