Question

Daily wages of 45 workers in a factory are given below:

Daily wages (in Rs)	100	125	150	175	200
Number of workers	6	8	9	12	10

Find the median and the mean.
Using empirical formula, calculate its mode.

Answer 1

$$\begin{gathered} \mathrm{Here},N\mathrm{is}45,\mathrm{which}\mathrm{is}\mathrm{odd}. \\ \mathrm{Median}=\left\{\left(\frac{N+1}{2}\right)\mathrm{th}\mathrm{observation}\right\} \\ =\left\{\frac{45+1}{2}\right\}\mathrm{observation} \\ =23\mathrm{th}\mathrm{observation} \\ \mathrm{Median}=150 \\ \mathrm{Mean}=\frac{\sum (f_{\mathrm{i}}\times {\mathit{x}}_{\mathrm{i}})}{\sum f_{\mathrm{i}}}=\frac{7050}{45}=156.67 \\ \mathrm{Mode}=3\left(\mathrm{Median}\right)-2\left(\mathrm{Mean}\right) \\ =3\left(150\right)-2(156.67) \\ =450-313.34 \\ =136.6 \end{gathered}$$

Hence, the median is 150, the mean is 156.67 and the mode is 136.6.