The mean and variance of 7 observations are 8 and 16 , respectively. If five observations are 2 , 4 , 10 , 12 , 14 then the absolute difference of the remaining two observations is :

Step-by-step solution

Assume, the two remaining observations are x and y x ¯ = 2 + 4 + 10 + 12 + 14 + x + y 7 = 8 ⇒    42 + x + y = 56 ⇒    x + y = 14       … … 1 σ 2 = Σ x 1 2 n - Σ x 1 n 2 16 = 4 + 16 + 100 + 144 + 196 + x 2 + y 2 7 - 8 2 ⇒    16 + 64 = 460 + x 2 + y 2 7 ⇒    560 = 460 + x 2 + y 2 ⇒    x 2 + y 2 = 100       … … 2 ⇒    x y = 48 , solving equations 1 &#