Following data shows the number of family members living in different bungalows of a locality: If the median number of members is found to be 5, find…

Number of members	Number of bungalows	Cumulative frequency
$\displaystyle 0$-$\displaystyle 2$	$\displaystyle 10$	$\displaystyle 10$
$\displaystyle 2$-$\displaystyle 4$	p	\(\displaystyle 10+\mathrm{p}\)
$\displaystyle 4$-$\displaystyle 6$	$\displaystyle 60$	\(\displaystyle 70+\mathrm{p}\)
$\displaystyle 6$-$\displaystyle 8$	q	\(\displaystyle 70+\mathrm{p}+\mathrm{q}\)
$\displaystyle 8$-$\displaystyle 10$	$\displaystyle 5$	\(\displaystyle 75+\mathrm{p}+\mathrm{q}\)
	$\displaystyle 120$

\[\begin{aligned} & 75+p+q=120 \\ & p+q=45 \end{aligned} \] Median is $\displaystyle 5$ ∴ Median class is $\displaystyle 4$-$\displaystyle 6$ \[5=4+\left[\frac{\dfrac{120}{2}-(10+\mathrm{p})}{60}\right] \times 2 \] On solving, we get \(\displaystyle \mathrm{p}=20\) and \(\displaystyle \mathrm{q}=25\)