Question

Find out the median size from the following:

Size	10−20	20−30	30−40	40−50
Frequency	42	25	58	40

Answer 1

Size	Frequency (f)	Cumulative Frequency (c.f.)
10 − 20 20 − 30	42 25	42 67
30 − 40	58 (f)	125
40 − 50	40	165
	$\underset{}{N=\sum }f=165$

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{165}{2}\right)}^{th}$ item, which is 82.5^th item.
This corresponds to the class interval of 30 − 40, so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{165}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=30+\frac{82.5-67}{58}\times 10 \\ \mathrm{or},\mathrm{Median}=30+2.67=32.67 \\ \mathrm{Thus},\mathrm{Median}=32.67 \end{gathered}$$