Question

Calculate the median from the following series:

Age (Years)	55−60	50−55	45−50	40−45	35−40	30−35	25−30	20−25
Number of Students	7	13	10	15	30	33	28	14

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	14 28 33 (f) 30 15 10 13 7	14 42 (c.f.) 75 105 120 130 143 150
	N = ∑f = 150

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{150}{2}\right)}^{th}$ item, which is 75^th item.
This corresponds to the class interval of (30 − 35), so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{150}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=30+\frac{75-42}{33}\times 5 \\ \mathrm{or},\mathrm{Median}=30+\frac{33}{33}\times 5 \\ \mathrm{Thus},\mathrm{Median}=35 \end{gathered}$$