The mean and variance of 7 observations are 8 and 16 respetively. If two observations are 6 and 8 , then the variance of the remaining 5 observations is :

Step-by-step solution

Let a ,   b ,   c ,   d ,   e be 5 unknown observations. Given that No. of observation, n = 7 , Mean = 8 , Variance = 16 ∴ sum of observations = No .  of   observation   × Mean = 7 × 8 = 56 ⇒ Mean of 5 remaining observations = 56 - 8 - 6 5 = 42 5 As, we know that, Variance for 7 observations = Σ x i 2 n - x ¯ 2 ⇒ 16 = Σ x i 2 7 - 64 ⇒ Σ x i 2 = 560 ⇒ a 2 + b 2 + c 2 + d 2 + e 2 + 64 + 36 = 560 ⇒ a 2 + b 2 + c 2 + d