Mathematics - Statistics Question with Solution | TestHub

Given:

Mean$=10$

$\Rightarrow \frac{7+10+11+15+a+b}{6}=10$

$\Rightarrow a+b=17 \dots \left(\mathrm{i}\right)$

And,

Variance$=\frac{20}{3}$

$\Rightarrow \frac{7^2+{10}^2+{11}^2+{15}^2+{\mathrm{a}}^2+{\mathrm{b}}^2}{6}-{10}^2=\frac{20}{3}$

$\Rightarrow \frac{495+{\mathrm{a}}^2+{\mathrm{b}}^2}{6}=\frac{320}{3}$

$\Rightarrow 495+{\mathrm{a}}^2+{\mathrm{b}}^2=640$

$\Rightarrow a^2+b^2=145 \dots \left(\mathrm{ii}\right)$

Solve $\left(i\right)$ and $\left(ii\right)$, we get

$a=9, b=8$ or $a=8, b=9$

$\therefore \left|a-b\right|=1$