Question

Find the variance for the set of data: 22, 26, 17, 20, 20.The variance is

Answer 1

The variance of a given data set with size N is given by the formula:

`\begin{gathered} \sigma=\sqrt{(1)/(N)\sum_(i=1)^N(x_i-\mu)^2} \\ Var(X)=\sigma^2 \end{gathered}`

Then, for the data set {22, 26, 17, 20, 20} and N = 5, we have:

`\begin{gathered} \mu=(22+26+17+20+20)/(5)=21 \\ \sigma=\sqrt{(1^2+5^2+(-4)^2+(-1)^2+(-1)^2)/(5)}=\sqrt{(44)/(5)}=2\sqrt{(11)/(5)} \\ \therefore Var(X)=(44)/(5)=8.8 \end{gathered}`