Question

Calcualte the mean of the following distribution of daily wages of workers in a factory:

Daily Wages (in ₹)	:	100-120	140-160	160-180	180-200	Total
No of Workers	:	10	30	15	5	80

Also, calculate the median for the distribution of wages given above.

Answer 1

Wages	Worker (f)	X	fX	c.f
100 – 120	10	110	1100	10
120-140	20	130	2600	30
140 – 160	30	150	4500	60
160 – 180	15	170	2550	75
180 – 200	5	190	950	80
	80		Ʃ fX = 11700

$$\begin{gathered} \overline{X}=\frac{\mathrm{\Sigma }fx}{\mathrm{\Sigma }f}=\frac{11700}{80}=146.25 \\ \mathrm{Median}\mathrm{class}\mathrm{is}\mathrm{given}\mathrm{by}\mathrm{the}\mathrm{size}\mathrm{of}{\left(\frac{N}{2}\right)}^{\mathrm{th}}\mathrm{item},\mathrm{i}.\mathrm{e}\mathrm{size}\mathrm{of}{\left(\frac{80}{2}\right)}^{\mathrm{th}},\mathrm{which}\mathrm{is}\mathrm{the}{40}^{\mathrm{th}}\mathrm{item}.\mathrm{This}\mathrm{corresponds}\mathrm{to}\mathrm{the}\mathrm{class}\mathrm{interval}140-160,\mathrm{so}\mathrm{this}\mathrm{is}\mathrm{the}\mathrm{median}\mathrm{class}. \\ M=l_1+\frac{{\left({\displaystyle \frac{N}{2}}\right)}^{\mathrm{th}}-c.f}{f}\times i \\ =140+\frac{40-30}{30}\times 20=140+6.66 \\ =146.66 \end{gathered}$$

Note: In the above calculation we have assumed a class interval (120-140) and its corresponding frequency as 20.