Question

50 students of economics, secured the following marks in an examination:

Marks	20−25	25−30	30−35	35−40	40−45	45−50	50−55	55−60	60−65	65−70
Students	6	3	7	4	6	4	2	8	3	7

Calculate median.

Answer 1

Marks	Student (f)	Cumulative Frequency (c.f.)
20 − 25 25 − 30 30 − 35 35 − 40 40 − 45 45 − 50 50 − 55 55 − 60 60 − 65 65 − 70	6 3 7 4 6(f) 4 2 8 3 7	6 9 16 20 (c.f.) 26 30 32 40 43 50
	N = ∑f = 50

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{50}{2}\right)}^{th}$ item, which is 25^th item.
This corresponds to the class interval of (40 − 45), so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{50}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=40+\frac{25-20}{6}\times 5 \\ \mathrm{or},\mathrm{Median}=40+\frac{25}{6} \\ \mathrm{Thus},\mathrm{Median}=40+4.16=44.16 \end{gathered}$$