If the mean of the following frequency distribution is 18, then find the missing frequency ' f '.

Class Interval	\(\displaystyle x_{i}\)	\(\displaystyle f_{i}\)	\(\displaystyle x_{i} f_{i}\)
$\displaystyle 11$-$\displaystyle 13$	$\displaystyle 12$	$\displaystyle 3$	$\displaystyle 36$
$\displaystyle 13$-$\displaystyle 15$	$\displaystyle 14$	$\displaystyle 6$	$\displaystyle 84$
$\displaystyle 15$-$\displaystyle 17$	$\displaystyle 16$	$\displaystyle 9$	$\displaystyle 144$
$\displaystyle 17$-$\displaystyle 19$	$\displaystyle 18$	$\displaystyle 13$	$\displaystyle 234$
$\displaystyle 19$-$\displaystyle 21$	$\displaystyle 20$	\(\displaystyle f\)	\(\displaystyle 20 f\)
$\displaystyle 21$-$\displaystyle 23$	$\displaystyle 22$	$\displaystyle 5$	$\displaystyle 110$
$\displaystyle 23$-$\displaystyle 25$	$\displaystyle 24$	$\displaystyle 4$	$\displaystyle 96$
		\(\displaystyle 40+f\)	\(\displaystyle 704+20 f\)

Mean \(\displaystyle =18 \Rightarrow \frac{\Sigma x_{i} f_{i}}{\Sigma f_{i}}=18\) \[\Rightarrow \frac{704+20 f}{40+f}=18 \Rightarrow 704+20 f=720+18 f \] \(\displaystyle 20 f-18 f=720-704 \Rightarrow 2 f=16\) \[f=8 \]