Question

Find out median, with the help of the following data:

Price Level	10−20	20−30	30−40	40−50	50−60	60−70
Number of Commodity	2	5	8	4	6	3

Answer 1

Price Level	No. of Commodity (f)	Cumulative Frequency (c.f.)
10 − 20 20 − 30 30 − 40 40 − 50 50 − 60 60 − 70	2 5 8(f) 4 6 3	2 7(c.f) 15 19 25 28
	N = ∑f = 28

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{28}{2}\right)}^{th}$ item, which is 14^th item.
This corresponds to the class interval of (30 − 40), so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{28}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=30+\frac{14-7}{8}\times 10 \\ \mathrm{or},\mathrm{Median}=30+\frac{7}{8}\times 10 \\ \mathrm{Thus},\mathrm{Median}=30+8.75=38.75 \end{gathered}$$