The mean of 5 observations is 5 and their variance is 12 . 4 . If...

\dfrac{x + y + 1 + 2 + 6}{5} = 5$</p><p>$⇒ x + y = 16$</p><p>Now$12.4 = \dfrac{\left(16 + 9 + 1 + {\left(x - 5\right)}^{2} + {\left(y - 5\right)}^{2}\right)}{5}$</p><p>$⇒ 62= 26 + {\left(x - 5\right)}^{2} + {\left(y - 5\right)}^{2}$</p><p>$⇒ 36 = {\left(x - 5\right)}^{2} + {\left(y - 5\right)}^{2}$</p><p>Shifting of the origin to \left(5, 5\right)$ 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 $x = 0 + 5 = 5 \text{ and } y = 6 + 5 = 11$

(or)

$x = 6 + 5 = 11 \text{\text{ and } }$ y = 0 + 5 = 5

Hence, the values of the remaining two are $5, 11$.