find the unbiased and biased standard deviation and variance

find the unbiased and biased standard deviation, and variance for 31, 42, 35, 55, 54, 34, 25, 44, 35. (show all work)

Solution

Find the unbiased and biased standard deviation, and variance for 31, 42, 35, 55, 54, 34, 25, 44, 35.

N=9

Sum=355

Sum of squares=14833

biased variance   = (14833-355*355/9)/9) =830.2222/9=92.25

biased SD= sqrt(92.25) =9.60

Unbiased variance   = (14833-355*355/9)/8) =830.2222/8=103.78

Unbiased SD= sqrt(103.78) =10.19