Question

Find out median wage rate from the following data-set:

Wage Rate (₹)	5−15	15−25	25−35	35−45	45−55	55−65
Number of Workers	4	6	10	5	3	2

Answer 1

Wages	No. of Worker (f)	Cumulative Frequency (c.f.)
5 − 15 15 − 25 25 − 35 35 − 45 45 − 55 55 − 65	4 6 10 5 3 2	4 10 20 25 28 30
	N = ∑f = 30

Median class is given by the size of ${\left(\frac{N}{2}\right)}^{th}$ item, i.e.${\left(\frac{30}{2}\right)}^{th}$ item, which is 15^th item.
This corresponds to the class interval of (25 − 35), so this is the median class.
$$\begin{gathered} \mathrm{Median}=l_1+\frac{{\displaystyle \frac{N}{2}}-c.f.}{f}\times i \\ \mathrm{so},\mathrm{Median}=l_1+\frac{{\displaystyle \frac{30}{2}}-c.f.}{f}\times i \\ \mathrm{or},\mathrm{Median}=25+\frac{15-10}{10}\times 10 \\ \mathrm{or},\mathrm{Median}=25+5 \\ \mathrm{Thus},\mathrm{Median}\mathrm{is}30 \end{gathered}$$