Find the missing frequency 'f' in the following table, if the mean of the given data is 18. Hence find the mode.

Daily Allowance	\(\displaystyle x_{i}\)	\(\displaystyle f_{i}\)	\(\displaystyle f_{i} x_{i}\)
$\displaystyle 11$-$\displaystyle 13$	$\displaystyle 12$	$\displaystyle 7$	$\displaystyle 84$
$\displaystyle 13$-$\displaystyle 15$	$\displaystyle 14$	$\displaystyle 6$	$\displaystyle 84$
$\displaystyle 15$-$\displaystyle 17$	$\displaystyle 16$	$\displaystyle 9$	$\displaystyle 144$
$\displaystyle 17$-$\displaystyle 19$	$\displaystyle 18$	$\displaystyle 13$	$\displaystyle 234$
$\displaystyle 19$-$\displaystyle 21$	$\displaystyle 20$	f	20f
$\displaystyle 21$-$\displaystyle 23$	$\displaystyle 22$	$\displaystyle 5$	$\displaystyle 110$
$\displaystyle 23$-$\displaystyle 25$	$\displaystyle 24$	$\displaystyle 4$	$\displaystyle 96$
Total		\(\displaystyle 44+\mathrm{f}\)	$\displaystyle 752$ + 20f

\[\begin{gathered} \text { Mean }=\frac{752+20 \mathrm{f}}{44+\mathrm{f}} \\ \Rightarrow 18=\frac{752+20 \mathrm{f}}{44+\mathrm{f}} \\ \therefore \mathrm{f}=20 \end{gathered} \] modal class is $\displaystyle 19$-$\displaystyle 21$ \[\begin{aligned} \text { mode } & =19+\frac{20-13}{40-13-5} \times 3 \\ & =19.95 \text { approx } . \end{aligned} \]