The mean square deviation of a set of n observation x ₁, x _ 2² , x _ n about a point c is defined as 1 n _ i=1 ^ n (x_ i -c )² The mean square deviations about -2 and 2 are 18 and 10 respectively, the standard deviation of this set of observations is

Step-by-step solution

We have 1 n _ i=1 ^ n (x_ i +2 )²=18 and array l 1 n _ i=1 ^ n (x_ i -2 )²=10 _ i=1 ^ n (x_ i +2 )²=18 n and array array l _ i=1 ^ n (x_ i -2 )²=10 n _ i=1 ^ n (x_ i +2 )²+ _ i=1 ^ n (x_ i -2 )²=28 n array and _ i=1 ^ n (x_ i +2 )²- _ i=1 ^ n (x_ i -2 )²=8 n array l 2 _ i=1 ^ n (x_ i +4 )²=28 n and 2 _ i=1 ^ n 4 x_ i =8 n _ i=1 ^ n x₁²+4 n=14 n and _ i=1 ^ n x_ i =n _ i=1 ^ n x_ i ²=10 n and _ i=1 ^ n x_ i =n = 1 n _ i=1 ^ n x_ i ²- ( 1 n _ i=1^ ^ n x_ i )² = 10 n n - ( n n )² =3 array