The mean and variance of 5 observations are 5 and 8 respectively. If 3 observations are 1 , 3 , 5 , then the sum of cubes of the remaining two observations is

Step-by-step solution

Let the two observations be a and b . Given: Mean = 5 ⇒ 1 + 3 + 5 + a + b 5 = 5 ⇒ a + b = 16                 … 1 And σ 2 = ∑ x i 2 5 - ∑ x i 5 2 ⇒ 8 = 1 2 + 3 2 + 5 2 + a 2 + b 2 5 - 25 ⇒ a 2 + b 2 = 130             … 2 Solving 1   &   2 , we get 16 - b 2 + b 2 = 130 ⇒ b = 9 So a = 7 Hence, a 3 + b 3 = 343 + 729 = 1072