Mathematics - Statistics Question with Solution | TestHub

Given, the data $x, y, 10, 12, 4, 6, 8, 12$.

So,

$\mathrm{Mean}=\frac{x+y+10+12+4+6+8+12}{8}$

$\Rightarrow 9=\frac{x+y+52}{8}$

$\Rightarrow x+y+52=72$

$\Rightarrow x+y=20$

And,

$\mathrm{Variance}=\left(\frac{\sum _{}{x}_i^2}{n}\right)-{\left(\frac{\sum _{}{x}_i}{n}\right)}^2$

$\Rightarrow 9.25=\left(\frac{x^2+y^2+100+144+16+36+64+144}{8}\right)-{\left(9\right)}^2$

$\Rightarrow x^2+y^2=218$

$\Rightarrow {\left(x+y\right)}^2-2xy=218$

$\Rightarrow {20}^2-2xy=218$

$\Rightarrow 2xy=182$

$\Rightarrow xy=91$

Now solving $x+y=20 \& xy=91$ we get,

$x=13, y=7\Rightarrow 3x-2y=25$