Question

what are the standard deviation and coefficient of variation of `{5,6,7,9,8}`?

Answer 1

Standard Deviation is `1.4142` and Coefficient of variation is `20.2%`

Explanation:

The mean `(mu)` of data set is given by the sum of data divided by their number i.e. `(Sigmax)/N`

Hence mean is `1/5(5+6+7+9+8)=7`

Standard Deviation `(sigma)` is given by `sqrt[(Sigmax^2)/N-((Sigmax)/N)^2`

`(Sigmax^2)/N=1/5(5^2+6^2+7^2+9^2+8^2)`

= `1/5(25+36+49+81+64)=255/5=51`

Hence Standard Deviation is `sqrt(51-(7)^2)=sqrt2=1.4142`

Coefficient of variation is `sigma/muxx100` = `1.4142/7xx100=20.2%`