Given data: $2,3,3,4,5,7,a,b$ (8 observations)

Mean $=4 \Rightarrow$ total sum $=8\times 4=32$
Sum of known terms $=24 \Rightarrow a+b=8$

Variance $=2 \Rightarrow \sum (x-4)^2=8\times 2=16$
Known contribution $=16 \Rightarrow (a-4)^2+(b-4)^2=0$
⇒ $a=b=4$

Data: $2,3,3,4,4,4,5,7$
Mode $=4$

Mean deviation about mode:
$=\frac{1}{8}[|2-4|+|3-4|+|3-4|+0+0+0+|5-4|+|7-4|]$
$=\frac{1}{8}[2+1+1+0+0+0+1+3]=\frac{8}{8}=1$