Question

Find the median of the following data:

Age	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60
No. Persons	50	70	100	180	150	120	70	60

Answer 1

Age	Frequency (f)	Cumulative Frequency (c.f.)
20 − 25 25 − 30 30 − 35	50 70 100	50 120 220 (c.f.)
35 − 40	180 (f)	400
40 − 45 45 − 50 50 − 55 55 − 60	150 120 70 60	550 670 740 800
	$\underset{}{N=\sum }f=800$

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{800}{2}\right)}^{th}$ item, which is 400^th item.
This corresponds to the class interval of 35 − 40, so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{800}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=35+\frac{400-220}{180}\times 5 \\ \mathrm{or},\mathrm{Median}=35+5=40 \\ \mathrm{Thus},\mathrm{Median}=40 \end{gathered}$$