The mean and variance of the data 4 , 5 , 6 , 6 , 7 , 8 , x , y where x < y are 6 and 9 4 respectively. Then x 4 + y 2 is equal to

Step-by-step solution

Mean = 4 + 5 + 6 + 6 + 7 + 8 + x + y 8 = 6 ⇒ x + y = 12                   … 1 Variance = ∑ x i 2 n - x ¯ 2 ⇒     9 4 = 4 2 + 5 2 + 6 2 + 6 2 + 7 2 + 8 2 + x 2 + y 2 8 - 6 2 ⇒     x 2 + y 2 = 80             … 2 On solving equations 1 and 2 , we get x 2 + 12 - x 2 = 80 ⇒    x 2 + 144 + x 2 - 24 x = 80 ⇒    2 x 2 - 24 x + 64 = 0 ⇒    x 2