Question

The following table shows the marks obtained by 41 students of a class.

Marks obtained	15	17	20	22	25	30
Number of students	2	5	10	12	8	4

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

Answer 1

$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{terms}\left(N\right)is41,\mathrm{which}\mathrm{is}\text{odd}. \\ \mathrm{Median}=\left\{\left(\frac{N+1}{2}\right)\mathrm{th}\mathrm{observation}\right\} \\ =\left\{21\mathrm{th}\mathrm{observation}\right\} \\ =22 \\ \mathrm{Median}=22 \\ \mathrm{Mean}=\frac{\sum \mathit{(}{f}_i\mathit{\times }{x}_i\mathit{)}}{\sum f_{\mathrm{i}}} \\ =\frac{899}{41} \\ \mathrm{Mean}=21.92 \\ \mathrm{Using}\mathrm{empirical}\mathrm{formula}: \\ \mathrm{Mode}=3\left(\mathrm{Median}\right)-2\left(\mathrm{Mean}\right) \\ =66-43.84 \\ \mathrm{Mode}=22.16 \end{gathered}$$

Hence, the median is 22, the mean is 21.92 and the mode is 22.16.