If mean and variance of 2, 3, 16, 20, 13, 7, x, y are 10 and 25 respectively, then xy =

It is given that

$\frac{2+3+16+20+13+7+x+y}{8}=10$ and

$\frac{1}{8}\left(2^2+3^2+{16}^2+{20}^2+{13}^2+7^2+x^2+y^2\right)-{10}^2=25$

$\Rightarrow x+y+61=80$ and $\frac{x^2+y^2+887}{8}=125$

$\Rightarrow x+y=19$ and $x^2+y^2=113$

$\Rightarrow (x+y{)}^2=361$ and $x^2+y^2=113$

$\Rightarrow x^2+y^2+2xy=361$ and $x^2+y^2=113$

$\Rightarrow x^2+y^2+2xy=361$ and $x^2+y^2=113$

$\Rightarrow 113+2xy=361\Rightarrow 2xy=248\Rightarrow xy=124$