Question

How to use the results of part (b) and appropriate computation formulas to compute the sample variances s2 and sample standard deviation s.

Answer 1

`s^2=\displaystyle\sum((x-\bar x)^2)/(n-1)=\frac1{n-1}\sum(x^2-2x\bar x+{\bar x}^2)=\frac{\displaystyle\sum x^2-2\bar x\sum x+{\bar x}^2}{n-1}`

where
`\bar x=22` is the mean. Since


`\sum x^2=2568`

`\sum x=110`

you have variance


`s^2=(2568-2(22)(110)+22^2)/(5-1)=37`

and so the standard deiviation is


`s=√(37)\approx6.083`