Question

What is the standard deviation of {2, 5, 9, 1, 1, 1, 3, 2, 7}?

Answer 1

`sigma=sqrt(1/9*(614/9))=2.753224821`

Explanation:

The formula for standard deviation `sigma` is

`sigma=sqrt(1/n*sum_(i=1)^n(x_i-mu)^2)" "` where `mu=`mean
`" "` `n=`number of items

Solve for the mean first

`mu=(2+5+9+1+1+1+3+2+7)/9=31/9=3.44444`

Compute the standard deviation `sigma`

`sigma=sqrt(1/n*sum_(i=1)^n(x_i-mu)^2)`

`sigma=sqrt(1/9*((2-31/9)^2+(5-31/9)^2+(9-31/9)^2+(1-31/9)^2+(1-31/9)^2+(1-31/9)^2+(3-31/9)^2+(2-31/9)^2+(7-31/9)^2)`

`sigma=sqrt(1/9*(614/9))=2.753224821`

God bless....I hope the explanation is useful.