Question

Find the median of the following data:

Valuable	0−10	10−20	20−30	30−40	40−50	50−60	60−70
Frequency	7	12	18	25	16	14	8

Answer 1

Variable	Frequency (f)	Cumulative Frequency (c.f.)
0 − 10 10 − 20 20 − 30	7 12 18	7 19 37 (c.f.)
30 − 40	25 (f)	62
40 − 50 50 − 60 60 − 70	16 14 8	78 92 100
	N=100

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{100}{2}\right)}^{\mathrm{th}}$ item, which is 50^th item.
This corresponds to the class interval of (30 − 40), so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=30+\frac{{\displaystyle \frac{100}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=30+\frac{50-37}{25}\times 10 \\ \mathrm{or},\mathrm{Median}=30+5.2=35.2 \\ \mathrm{Thus},\mathrm{median}=35.2 \end{gathered}$$