$5=\bar{x}=\frac{\sum x_i f_i}{\sum f_i}=\frac{4+72+140+7 \alpha+72}{64+\alpha}$

$\Rightarrow 320+5 \alpha=288+7 \alpha \Rightarrow 2 \alpha=32 \Rightarrow \alpha=16$

$\text { M.. }(\bar{x})=\frac{\sum f _{ i }\left| x _{ i }-\overline{ x }\right|}{\sum f _{ i }} \text { where } \sum f _{ i }=64+16=80$

$\text { M.D. }(\bar{x})=\frac{4 \times 4+24 \times 2+28 \times 0+16 \times 2+8 \times 4}{80}$

$=\frac{8}{5}$

$\text { Variance }=\frac{\sum f _{ i }\left( x _{ i }-\overline{ x }\right)^2}{\sum f _{ i }}$

$=\frac{4 \times 16+24 \times 4+0+16 \times 4+8 \times 16}{80}=\frac{352}{80}$

$\therefore \frac{3 \alpha}{m+\sigma^2}=\frac{3 \times 16}{\frac{128}{80}+\frac{352}{80}}=8$