If both the mean and the standard deviation of 50 observations x 1 , x 2 , … , x 50 are equal to 16 , then the mean of x 1 - 4 2 , x 2 - 4 2 , … , x 50 - 4 2 is

Step-by-step solution

For observations x 1 ,   x 2 ,   . . . . . . . . . . . x 50 We have, mean, x ¯ = ∑ x i   50 = 16       . . . . . i And, standard deviation, σ = ∑ x i 2 50 - x ¯ 2 = 16 ⇒ ∑ x i 2 50 = 16 2 + x ¯ 2 ⇒ ∑ x i 2 50 = 16 2 + 16 2 = 512     . . . . . i i Now, the mean value of x 1 - 4 2 ,   x 2 - 4 2 ,   . . . ,   x 50 - 4 2 will be = ∑ x i - 4 2 50 = ∑ x i 2 - 8   ∑ x i + 16 × 50 5