The mean and variance for seven observations are 8 and 16 respectively. If 5 of the observations are 2 , 4 , 10 , 12 , 14 , then the product of the remaining two observations is

Step-by-step solution

Let the remaining two observations are x and y . Mean   x ¯ = ∑ x i N = 2 + 4 + 10 + 12 + 14 + x + y 7 ⇒   42 + x + y 7 = 8 ⇒ x + y = 14           . . . 1 Variance, σ 2 = ∑ x i 2 N - x ¯ 2 = 4 + 16 + 100 + 144 + 196 + x 2 + y 2 7 - 64   ⇒ σ 2 = 460 + x 2 + y 2 7 - 64 = 16 ⇒ x 2 + y 2 = 100         … 2 From 1 and 2 , we get, x = 6 , y = 8 and x y = 48