Question

Find the variance for the set of data: 22,28,15,20,20The variance is

Answer 1

First, we calculate the mean.

`\bar{x}=(\sum_^x_i)/(n)=(22+28+15+20+20)/(5)=21`
`\begin{gathered} \sigma^2=\frac{\sum_^(x_i-\bar{x})^2}{n-1} \\ \\ \sigma^2=(\sum_^(x_i-21)^2)/(4)=((22-21)^2+(28-21)^2+(15-21)^2+(20-21)^2+(20-21)^2)/(4) \\ \\ \Rightarrow\sigma^2=(1+49+36+1+1)/(4)=(88)/(4)=22 \end{gathered}`

Therefore, Variance = 22