The following distribution shows the daily pocket allowance of children of a locality. The mean daily pocket allowance is ₹ $\displaystyle 36 \cdot 10$. Find the missing frequency, f.
Daily pocket allowance (in ₹) $\displaystyle 20$-$\displaystyle 25$ $\displaystyle 25$-$\displaystyle 30$ $\displaystyle 30$-$\displaystyle 35$ $\displaystyle 35$-$\displaystyle 40$ $\displaystyle 40$-$\displaystyle 45$ $\displaystyle 45$-$\displaystyle 50$ $\displaystyle 50$-$\displaystyle 55$
Number of children $\displaystyle 7$ $\displaystyle 6$ $\displaystyle 9$ $\displaystyle 13$ f $\displaystyle 5$ $\displaystyle 4$

Daily pocket allowance (in ₹)	Number of children \(\displaystyle \left(f_{i}\right)\)	\(\displaystyle x_{i}\)	\(\displaystyle x_{i} f_{i}\)
$\displaystyle 20$-$\displaystyle 25$	$\displaystyle 7$	$\displaystyle 22.5$	$\displaystyle 157.5$
$\displaystyle 25$-$\displaystyle 30$	$\displaystyle 6$	$\displaystyle 27.5$	$\displaystyle 165$
$\displaystyle 30$-$\displaystyle 35$	$\displaystyle 9$	$\displaystyle 32.5$	$\displaystyle 292.5$
$\displaystyle 35$-$\displaystyle 40$	$\displaystyle 13$	$\displaystyle 37.5$	$\displaystyle 487.5$
$\displaystyle 40$-$\displaystyle 45$	f	$\displaystyle 42.5$	$\displaystyle 42.5$ f
$\displaystyle 45$-$\displaystyle 50$	$\displaystyle 5$	$\displaystyle 47.5$	$\displaystyle 237.5$
$\displaystyle 50$-$\displaystyle 55$	$\displaystyle 4$	$\displaystyle 52.5$	$\displaystyle 210.0$
Total	\(\displaystyle 44+\mathrm{f}\)		$\displaystyle 1550$ + $\displaystyle 42.5$ f

Marking-scheme solution