Question

Calculate the median from the following data:

Marks	Frequency
Less than 10	5
Less than 20	20
Less than 30	45
Less than 40	80
Less than 50	100
Less than 60	115
Less than 70	125
Less than 80	130

Answer 1

Marks	Class Interval	Frequency (f)	Cumulative Frequency (c.f.)
Less than 10 Less than 20 Less than 30	0 − 10 10 − 20 20 − 30	5 15 25	5 20 45 c.f
Less than 40	30 − 40	(f) 35	80
Less than 50 Less than 60 Less than 70 Less than 80	40 − 50 50 − 60 60 − 70 70 − 80	20 15 10 5	100 115 125 130
		$\underset{}{N=\sum }f=130$

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{130}{2}\right)}^{\mathrm{th}}$ item, which is 65^th item.
This corresponds to the class interval of 30 − 40, so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{130}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=30+\frac{65-45}{35}\times 10 \\ \mathrm{or},\mathrm{Median}=30+5.71=35.71 \\ \mathrm{Thus},\mathrm{Median}=35.71 \end{gathered}$$