The mean of the numbers a, b, 8,5,10 is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25 M is equal to:

$\begin{array}{l}{\sigma }^2=\frac{\sum _{i=1}^5 {\left(x_i-\overline{x}\right)}^2}{n}\\ \text{ Mean }=6\\ \frac{\mathrm{a}+\mathrm{b}+8+5+10}{5}=6\Rightarrow a+b=7\\ a+b=7\\ \mathrm{b}=7-\mathrm{a}\\ 6.8=\frac{(a-6{)}^2+(b-6{)}^2+(8-6{)}^2+(5-6{)}^2+(10-6{)}^2}{5}\\ 34=(a-6{)}^2+(7-a-6{)}^2+4+1+18\\ {\mathrm{a}}^2-7\mathrm{a}+12=0\Rightarrow \mathrm{a}=4\text{ or }\mathrm{a}=3\\ a=4a=3\\ \mathrm{b}=3\mathrm{b}=4\\ M=\frac{\sum _{i=1}^5 \left|x_i-x\right|}{n}\\ M=\frac{|a-6|+|b-6|+|8-6|+|5-6|+|10-6|}{5}\\ \begin{array}{ll}\text{ when }\mathrm{a}=3,\mathrm{b}=4& \text{ when }\mathrm{a}=4,\mathrm{b}=3\\ \mathrm{M}=\frac{3+2+2+1+4}{5}& \mathrm{M}=\frac{2+3+2+1+7}{5}\end{array}\\ M=\frac{12}{5}M=\frac{12}{5}\Rightarrow 25\mathrm{M}=25\times \frac{12}{5}=60\end{array}$