The mean and variance for seven observations are 8 and 16...

Let the remaining two observations are $x$ and $y$.

Mean $\overset{¯}{x} = \dfrac{∑ {x}_{i}}{N} = \dfrac{2 + 4 + 10 + 12 + 14 + x + y}{7}$

$⇒ \dfrac{42 + x + y}{7} = 8$

$⇒ x + y = 14 . . . \left(1\right)$
Variance,

${\sigma}^{2} = \dfrac{∑ {x}_{i}^{2}}{N} - {\left(\overset{¯}{x}\right)}^{2} = \dfrac{4 + 16 + 100 + 144 + 196 + {x}^{2} + {y}^{2}}{7} - 64$

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

$⇒ {x}^{2} + {y}^{2} = 100 \ldots$\left(2\right)$</p><p>From \left(1\right)$ and \left(2\right)$, we get,</p><p>$x = 6, y = 8$and$xy = 48