Find the mean, variance and the standard deviation for the following data :
5,9,8,12,6,10,6,8

Explanation

Here n=8.
`"Mean, "barx=(1)/(8)(5+9+8+12+6+10+6+8)=(64)/(8)=8.`
The values of `(x_(i)-barx)` are
`-3,1,0,4,-2,2,-2,0.`
`therefore" "(x_(i)-bar)^(2)=(9+1+0+16+4+4+4+0)=38.`
`therefore" variance," sigma^(2)=(Sigma(x_(i)-barx)^(2))/(n)=(38)/(8)=(19)/(4)=4.75.`
and, standard deviation, `sigma=(8)/sqrt(4.75)=2.17.`
`therefore" "`mean=8, variance =4.75 and standard deviation =2.17.