Question

Age (in years)	$10-20$	$20-30$	$30-40$	$40-50$	$50-60$	$60-70$
No. of patients	$60$	$42$	$55$	$70$	$53$	$20$

The following table shows ages of $300$ patients getting medical treatment in a hospital on a particular day. Find the median.

Answer 1

Classes (Age in years)	Frequency $\left(f_i\right)$ (No. of patients)	Cumulative frequency less than type
10-20	60	60
20-30	42	102 $\to$ c.f
30-40	55 $\to$f	157
40-50	70	227
50-60	53	280
60-70	20	300
Total	300 $\to$ N

a

Here total frequency, $\sum f_i=N=300$

$\therefore \frac{N}{2}=\frac{300}{2}=150$

Cumulative frequency, which is just greater than $150$ is $157$.

Therefore, corresponding class $30-40$ is the median class.

$L=30,N=300,c.f.102,f=55,h=10$

Median $=L+(\frac{N}{2}-c.f.)\frac{h}{f}$

$=30+(150-102)\frac{10}{55}$

$=30+48\times \frac{10}{55}$

$=30+\frac{96}{11}=30+8.73=38.73$

Hence, median $=38.73$ years.