The mean and the variance of five observations are 4 and 5.20 ,...

Let rest two observations are $x$ and $y$.

Given mean $= 4$

$⇒ \dfrac{3 + 4 + 4 + x + y}{5} = 4 ⇒ x + y = 9 . . . \left(1\right)$

Given variance $= 5 . 2$

$⇒ \dfrac{9 + 16 + 16 + {x}^{2} + {y}^{2}}{5} - {\left(4\right)}^{2} = 5 . 2$

$⇒ {x}^{2} + {y}^{2} = 65 . . . \left(2\right)$

Squaring equation \left(1\right)$and subtracting equation \left(2\right)$, we get

$2xy = 81 - 65 ⇒ 2xy = 16 ⇒ xy = 8$

$∴ {\left(x - y\right)}^{2} = {x}^{2} + {y}^{2} - 2xy = 65 - 16 = 49$

$∴ \left|x - y\right| = 7$