Question

The following table shows the frequency distribution of amount of bonus paid to the workers in a certain factory.

Bonus paid (in Rs.)	Below 500	Below 600	Below 700	Below 800	Below 900	Below 1000	Below 1100
No. of workers	4	12	24	41	51	58	60

Find the median amount of bonus paid to the workers.

Answer 1

Bonus paid (in Rs.)	Cumulative frequency (less than type)	Class intervals	Frequency
Below 500	4	0-500	4
Below 600	12	500-600	8
Below 700	24	600-700	12
Below 800	41	700-800	17
Below 900	51	800-900	10
Below 1000	58	900-1000	7
Below 1100	60	1000-1100	2

$$\begin{gathered} \mathrm{Total}\mathrm{frequency}=\sum _{}^{}{f}_i=N=60 \\ \therefore \frac{N}{2}=\frac{60}{2}=30 \\ \mathrm{So},\text{the}\mathrm{cumulative}\mathrm{frequency}\mathrm{should}\mathrm{be}\mathrm{just}\mathrm{greater}\mathrm{than}\mathrm{or}\mathrm{equal}\mathrm{to}30,\mathrm{i}.\mathrm{e}.41. \\ \mathrm{Therefore},\mathrm{the}\mathrm{median}\mathrm{class}\mathrm{will}\mathrm{be}700-800. \\ \mathrm{Median}=L+\left(\frac{N}{2}-c.f.\right)\frac{h}{f} \\ \mathrm{Here},L=\mathrm{lower}\mathrm{limit}\mathrm{of}\mathrm{the}\mathrm{median}\mathrm{class}=700 \\ c.f.=\mathrm{cumulative}\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{class}\mathrm{preceeding}\mathrm{the}\mathrm{median}\mathrm{clas}s=24 \\ h=\mathrm{width}\mathrm{of}\mathrm{the}\mathrm{median}\mathrm{class}=100 \\ f=\mathrm{frequency}\mathrm{of}\mathrm{the}\mathrm{median}\mathrm{class}=(41-24)=17 \\ \therefore \mathrm{Median}=700+\left(30-24\right)\frac{100}{17} \\ =700+6\times 5.88 \\ =700+35.29 \\ =735.29 \\ \therefore \mathrm{Median}\mathrm{amount}\mathrm{of}\mathrm{bonus}\mathrm{paid}\mathrm{to}\text{the}\mathrm{workers}\mathrm{is}\mathrm{Rs}735.29. \end{gathered}$$