Let the mean and variance of four numbers 3 , 7 , x and y ( x > y ) be 5 and 10 respectively. Then the mean of four numbers 3 + 2 x , 7 + 2 y , x + y and x - y is ______.

Step-by-step solution

Mean = 5 , Variance = 10 3 + 7 + x + y 4 = 5 , 10 = ∑ x i 2 4 - ∑ x 2 10 + x + y = 20 ,    10 = ∑ x i 2 4 - 25 x + y = 10 y = 10 - x ,    40 = ∑ x i 2 - 100 140 = ∑ x i 2 140 = 9 + 49 + x 2 + y 2 140 = 58 + x 2 + y 2 x 2 + y 2 = 82 x + y 2 = x 2 + y 2 + 2 x y 100 - 82 = 2 x y 18 = 2 x y x y = 9 x 10 - x = 9 ⇒ x 2 - 10 x + 9 = 0 = x = 1 , 9 y = 9 , 1 As x > y So, x = 9 ,   y = 1 x ¯ = 3 + 2 x + 7 + 2 y + x + y + x - y 4 ⇒ 10 + 4 x + 2 y 4 &#