Consider the following frequency distribution 

 If mean $\frac{309}{22}$  and median is 14 then the value of ${(a-b)}^2$  equal to ____
 

$mean=\frac{504+3a+9b}{26+a+b}=\frac{309}{22}$  $243a+111b=3054$  $81a+37b=1018$

Median class is  $12-18$  $median=12+\frac{\frac{a+b+26}{2}-(a+b)}{12}\times 6=14$  $\frac{a+b+26-2a-2b}{2}=4\Rightarrow a+b=18$  $\therefore a=8b=10\Rightarrow {(a-b)}^2=4$