Question:
The median of the following data is 50. Find the values of p and q, if the sum of all the frequencies is 90.
Solution:
Given $N=90$
$\therefore$ $\frac{N}{2}=\frac{90}{2}=45$
which lies in the interval $50-60$.
Lower limit, $l=50, f=20, c f=40+p, h=10$
$\therefore$ Median $=l+\frac{\left(\frac{N}{2}-c f\right)}{f} \times h$
$=50+\frac{(45-40-\rho)}{20} \times 10$
$\Rightarrow$ $50=50+\left(\frac{5-p}{2}\right)$
$\Rightarrow$ $0=\frac{5-p}{2}$
$\therefore$ $p=5$
Also, $78+p+q=90$ [given]
$\Rightarrow \quad 78+5+q=90$
$\Rightarrow \quad q=90-83$
$\therefore \quad \quad q=7$