The mean and variance of a data set comprising 15 observations are 15 and 5 respectively. If one of the observation 15 is deleted and two new observations 6 and 8 are added to the data, then the new variance of resulting data is

Step-by-step solution

Let 15 observations are x 1 , x 2 … … x 15 x 1 + x 2 + x 3 … … x 15 15 = 15 If x 15 = 15 x ¯ new = x 1 + x 2 + x 3 … x 15 - 15 + 6 + 8 16 = 224 16 = 14 Σ x i 2 15 - x ¯ 2 = 5 ⇒   x 1 2 + x 2 2 … … x 14 2 + 15 2 = 230 × 15 ⇒     x 1 2 + x 2 2 … … x 14 2 = 3225 New variance = x 1 2 + x 2 2 … … x 14 2 + 6 2 + 8 2 16 - x ¯ new 2 = 3325 16 - 196 =   11 . 8125