Thank you for reporting, we will resolve it shortly
Q.
The mean and variance of $8 $ observations are $10$ and $13.5,$ respectively. If $6$ of these observations are $5,7,10,12,14,15,$ then the absolute difference of the remaining two observations is :
$\bar{x}=10$
$\Rightarrow \bar{x}-\frac{63+a+b}{8}=10$
$ \Rightarrow a+b=17\dots$(1)
Since, variance is independent of origin.
So, we subtract 10 from each observation.
So, $\sigma^{2}=13.5=\frac{79+(a-10)^{2}+(b-10)^{2}}{8}-(10-10)^{2}$
$\Rightarrow a^{2}+b^{2}-20(a+b)=-171$
$\Rightarrow a^{2}+b^{2}=169 \dots$(2)
From (i) $\&$ (ii); $a=12 \& b=5$