If the mean of a set of observations x 1 , x 2 , x 3 , . . . . , x n is x ¯ , then the mean of observations x i + 2 i ,   ∀ i = 1,2 , 3 , . . . . n is equal to

Step-by-step solution

Given, n x ¯ = x 1 + x 2 + x 3 + . . . + x n Now, new observations are x 1 + 2 , x 2 + 2.2 , . . . . x n + 2 . n ∴ new mean = x 1 + 2 + x 2 + 2.2 + x 3 + 2.3 + . . . . + x n + 2 . n n = x 1 + x 2 + x 3 + . . . + x n n + 2 1 + 2 + 3 + . . . + n n = x ¯ + 2 n + 1 2