If both mean and variance of 50 observations x₁, x₂, , x₅₀ are equal to 16 and 256 respectively, then mean of (x₁-5 )^2, (x₂-5 )^2, (x₅₀-5 )^2 is

Step-by-step solution

Given that n =50, x =16 and _x ^2=256 array ll & _x^2= 1 n ( _ i=1 ⁵⁰ x_i^2 )-( x )^2 & 256= 1 50 ( _ i=1 ⁵⁰ x_i^2 )-256 & 1 50 ( _ i=1 ⁵⁰ x_i^2 )=512 & _ i=1 ⁵⁰ x_i^2=25600 array Now aligned _ i=1 ^5 (x_i-5 )^2 & = _ i=1 ⁵⁰ x_i^2+25 50-10 _ i=1 ^5 x_i & =25600+1250-8000 aligned ... [From (i) and (ii)] 18850 Required Mean = _ i=1 ⁵⁰ (x_i-5 )^2 50 = 18850 50 =377