The mean and the variance of five observations are 4 and 5.20 , respectively. If three of the observations are 3 , 4 and 4 ; then the absolute value of the difference of the other two observations, is :

Step-by-step solution

Let rest two observations are x and y . Given mean = 4 ⇒ 3 + 4 + 4 + x + y 5 = 4 ⇒ x + y = 9           . . . 1 Given variance = 5 . 2 ⇒ 9 + 16 + 16 + x 2 + y 2 5 - 4 2 = 5 . 2 ⇒ x 2 + y 2 = 65           . . . 2 Squaring equation 1 and subtracting equation 2 , we get 2 x y = 81 - 65 ⇒ 2 x y = 16 ⇒ x y = 8 ∴   x - y 2 = x 2 + y 2 - 2 x y = 65 - 16 = 49 ∴   x - y = 7