Question

If the mean and variance of eight numbers $3,7,9,12,13,20,x$ and $y$ be $10$ and $25$ respectively, then $xy$ is equal to

Answer 1

Mean $=\frac{64+x+y}{8}=10$
$\Rightarrow x+y=16$

Variance $=\frac{\sum x_i^2}{n}-(\overline{x}{)}^2$
$\Rightarrow 25=\frac{3^2+7^2+9^2+{12}^2+{13}^2+{20}^2+x^2+y^2}{8}-100\Rightarrow 1000=852+x^2+y^2\Rightarrow x^2+y^2=148\Rightarrow (x+y{)}^2-2xy=148\Rightarrow 256-2xy=148\therefore xy=54$