Mathematics - Statistics Question with Solution | TestHub

Mean$=\stackrel{-}{\mathrm{x}}=\frac{3+7+9+12+13+20+x+y}{8}=10\Rightarrow x+y=16\dots \left(\mathrm{i}\right)$
Variance${\sigma }^2=\frac{\sum {\left(x_i\right)}^2}{8}-{\left(\stackrel{-}{\mathrm{x}}\right)}^2=25$
$\frac{9+49+81+144+169+400+x^2+y^2}{8}-100=25$
$\Rightarrow x^2+y^2=148\dots \left(\mathrm{i}\mathrm{i}\right)$
${\left(x+y\right)}^2={\left(16\right)}^2=x^2+y^2+2xy=256\Rightarrow xy=54$