Question

Data relating to wages of some workers are given below. Find out median wage.

Wages (₹)	20−30	30−40	40−50	50−60	60−70
Number of Workers	25	12	15	13	5

Answer 1

Wages	No. of Workers (F)	Cumulative Frequency (c.f.)
20 − 30 30 − 40 40 − 50 50 − 60 60 − 70	25 12 (f) 15 13 5	25 37 52 65 70
	N = ∑f = 70

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{70}{2}\right)}^{th}$ item, which is 35^th item.
This corresponds to the class interval of 30 − 40, so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{70}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=30+\frac{35-25}{12}\times 10 \\ \mathrm{or},\mathrm{Median}=30+\frac{100}{12} \\ \mathrm{Thus},\mathrm{Median}=30+8.33=38.33 \end{gathered}$$