$\sigma^{2}=\frac{\sum\limits_{i=1}^{5}\left(x_{i}-\bar{x}\right)^{2}}{n}$

Mean $=6$

$\frac{a+b+8+5+10}{5}=6$

$a+b=7$

$b=7-a$

$6.8=\frac{(a-6)^{2}+(b-6)^{2}+(8-6)^{2}+(5-6)^{2}+(10-6)^{2}}{5}$

$34=(a-6)^{2}+(7-a-6)^{2}+4+1+18$

$a^{2}-7 a+12=0 \Rightarrow a=4$ or $a=3$

$a=4 \quad a=3$

$b=3 \quad b=4$

$M=\frac{\sum\limits_{i=1}^{5}\left|x_{i}-x\right|}{n}$

$M=\frac{|a-6|+|b-6|+|8-6|+|5-6|+|10-6|}{5}$

when $a =3, b =4 \quad$ 

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

$M =\frac{12}{5}$

when $a =4, b =3$

$ M =\frac{2+3+2+1+7}{5}$

$M =\frac{12}{5}$

$25\;M =25 \times \frac{12}{5}=60$