Find the mean of the following distribution :
Classes $\displaystyle 0$-$\displaystyle 15$ $\displaystyle 15$-$\displaystyle 30$ $\displaystyle 30$-$\displaystyle 45$ $\displaystyle 45$-$\displaystyle 60$ $\displaystyle 60$-$\displaystyle 75$ $\displaystyle 75$-$\displaystyle 90$
Frequency $\displaystyle 17$ $\displaystyle 20$ $\displaystyle 18$ $\displaystyle 21$ $\displaystyle 15$ $\displaystyle 9$

Classes	x	f	\(\displaystyle \mathrm{u}=\frac{x-52 \cdot 5}{15}\)	fu
$\displaystyle 0$-$\displaystyle 15$	\(\displaystyle 7 \cdot 5\)	$\displaystyle 17$	- $\displaystyle 3$	-$\displaystyle 51$
$\displaystyle 15$-$\displaystyle 30$	\(\displaystyle 22 \cdot 5\)	$\displaystyle 20$	-$\displaystyle 2$	-$\displaystyle 40$
$\displaystyle 30$-$\displaystyle 45$	\(\displaystyle 37 \cdot 5\)	$\displaystyle 18$	-$\displaystyle 1$	-$\displaystyle 18$
$\displaystyle 45$-$\displaystyle 60$	\(\displaystyle 52 \cdot 5\)	$\displaystyle 21$	$\displaystyle 0$	$\displaystyle 0$
$\displaystyle 60$-$\displaystyle 75$	\(\displaystyle 67 \cdot 5\)	$\displaystyle 15$	$\displaystyle 1$	$\displaystyle 15$
$\displaystyle 75$-$\displaystyle 90$	\(\displaystyle 82 \cdot 5\)	$\displaystyle 9$	$\displaystyle 2$	$\displaystyle 18$
		$\displaystyle 100$		-$\displaystyle 76$

Marking-scheme solution