If the mean and standard deviation of 5 observations x 1 , x 2 , x 3 , x 4 , x 5 are 10 and 3 , respectively, then the variance of 6 observations x 1 , x 2 , … , x 5 and - 50 is equal to

Step-by-step solution

We have, Mean = x 1 + x 2 + x 3 + x 4 + x 5 5 = 10 ⇒ x 1 + x 2 + x 3 + x 4 + x 5 = 50       . . . i   Variance = S . D 2 = Σ x i 2 5 - x ¯ 2 = 9 ⇒ x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 5 - 100 = 9 ⇒ x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 = 545       . . . ii   Now, x ¯ n e w = x 1 + x 2 + x 3 + x 4 + x 5 - 50 6 = 0 New variance = ∑ i = 1 6 x i 2 6 - x ¯ n e w 2   = x 1 2 + x 2 2 + x 3 2 + x 4 2 + x 5 2 + 2500 6 - 0 = 545 + 2500