For what value of x, is the median of the following frequency distribution $\displaystyle 34$•$\displaystyle 5$ ?

Class	Frequency	c.f.
$\displaystyle 0$-$\displaystyle 10$	$\displaystyle 3$	$\displaystyle 3$
$\displaystyle 10$-$\displaystyle 20$	$\displaystyle 5$	$\displaystyle 8$
$\displaystyle 20$-$\displaystyle 30$	$\displaystyle 11$	$\displaystyle 19$
$\displaystyle 30$-$\displaystyle 40$	$\displaystyle 10$	$\displaystyle 29$
$\displaystyle 40$-$\displaystyle 50$	$\displaystyle x$	$\displaystyle 29+x$
$\displaystyle 50$-$\displaystyle 60$	$\displaystyle 3$	$\displaystyle 32+x$
$\displaystyle 60$-$\displaystyle 70$	$\displaystyle 2$	$\displaystyle 34+x$
$\displaystyle \therefore 34 \cdot 5=30+\frac{10}{10}\left(\frac{34+x}{2}-19\right)$
$\displaystyle \Rightarrow x=13$

Marking-scheme solution