Question

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

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

• A. $33.73$ years
• B. $38.73$ years
• C. $42.37$ years
• D. $44.73$ years

Answer 1

Answer: (B)

$38.73$ years

Consider the following table, to calculate median:

$c_i$	$f_i$	$cf$
10-20	60	60
20-30	42	60+42=102
30-40	55	102+55=157
40-50	70	157+70=227
50-60	53	227+53=280
60-70	20	280+20=300

Median $=l+\frac{(\frac{N}{2}-cf)}{f_m}\times c$

Here,

Class Interval $c=10$

$N=\Sigma f_i=300$

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

$\Rightarrow$ Median class $=30-40$

$\Rightarrow$Frequency of median class$f_m=55$

Lower boundary of median class $l=30$

previous cumulative frequency of median class $cf=102$

$\therefore$ Median $=30+\frac{(\frac{300}{2}-102)}{55}\times 10$

$\therefore$ Median $=30+\frac{\left(48\right)}{55}\times 10$

$\therefore$ Median $=38.727\Rightarrow 38.73$

Hence. option $B$ is correct.