The mean and variance of 7 observations are 8 and 16 ,...

$\overset{¯}{x} = \dfrac{2 + 4 + 10 + 12 + 14 + x + y}{7} = 8$

$⇒ 42 + x + y = 56$

$⇒ x + y = 14 \ldots \ldots \left(1\right)$

${\sigma}^{2} = \dfrac{Σ{x}_{1}^{2}}{n} - {\left(\dfrac{Σ{x}_{1}}{n}\right)}^{2}$

$16 = \dfrac{4 + 16 + 100 + 144 + 196 + {x}^{2} + {y}^{2}}{7} - {\left(8\right)}^{2}$

$⇒ 16 + 64 = \dfrac{460 + {x}^{2} + {y}^{2}}{7}$

$⇒ 560 = 460 + {x}^{2} + {y}^{2}$

$⇒ {x}^{2} + {y}^{2} = 100 \ldots \ldots \left(2\right)$

$⇒ xy = 48$, solving equations \left(1\right) \text{ and } \left(2\right)$</p><p>${\left(x - y\right)}^{2} = {\left(x + y\right)}^{2} - 4xy = 4$</p><p>$∴ \left|x - y\right| = 2