Mathematics - Statistics Question with Solution | TestHub

Mean $\overline{x}=\frac{a+6+8+5+10}{5}=6$ (given) 

$\Rightarrow a+b=7 ...\left(\mathrm{i}\right)$

Variance $=\frac{\sum x_i^2}{n}-{\left(\overline{x}\right)}^2=\frac{a^2+b^2+8^2+5^2+{10}^2}{5}-6^2=6.8$ (given)

$\Rightarrow a^2+b^2=25 ...\left(\mathrm{ii}\right)$

on solving equations $\left(\mathrm{i}\right)$ & $\left(\mathrm{ii}\right)$, we get $a=3, b=4$

Now, Mean deviation about Mean $M=\frac{\sum \left|x_i-\overline{x}\right|}{n}$

$\Rightarrow \frac{\left|3-6\right|+\left|4-6\right|+\left|8-6\right|+\left|5-6\right|+\left|10-6\right|}{5}$

$\Rightarrow \frac{3+2+2+1+4}{5}=\frac{12}{5}$

$\therefore M=\frac{12}{5}\Rightarrow 25M=60$.