Question

Given the following data, find out median:

Age	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60
Number of Students	50	70	100	180	150	120	70	60

Answer 1

Age	No. of Students (f)	Cumulative Frequency (c.f.)
20 − 25 25 − 30 30 − 35 35 − 40 40 − 45 45 − 50 50 − 55 55 − 60	50 70 100 180 (f) 150 120 70 60	50 120 220 (c.f.) 400 550 670 740 800
	N = ∑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.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{800}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=35+\frac{400-220}{180}\times 5 \\ \mathrm{or},\mathrm{Median}=35+\frac{180}{180}\times 5 \\ \mathrm{Thus},\mathrm{Median}=35+5=40 \end{gathered}$$