The mean of 5 observations is 5 and their variance is 12 . 4 . If three of the observations are 1 , 2 & 6 ; then the value of the remaining two is :

Step-by-step solution

x + y + 1 + 2 + 6 5 = 5 ⇒ x + y = 16 Now 12.4 = 16 + 9 + 1 + x - 5 2 + y - 5 2 5 ⇒ 62  = 26 + x - 5 2 + y - 5 2 ⇒ 36 = x - 5 2 + y - 5 2 Shifting of the origin to 5 , 5 the equations will become 6 2 = x 2 + y 2 and x + y = 6 Solving them and again will get the x = 0 or y = 0 . If x = 0 ⇒ y = 6 or If y = 0 ⇒ x = 6 . But by shifting the origin back to original position, we get x = 0 + 5 = 5   &   y = 6 + 5 = 11 (or) x = 6 + 5 = 11   &   y = 0 + 5 = 5 Henc