Question

The following table shows the weight of 12 players:

Weight (in kg)	48	50	52	54	58
Number of players	4	3	2	2	1

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

Answer 1

We will prepare the table given below:



$$\begin{gathered} \mathrm{Number}\mathrm{of}\mathrm{terms}\left(N\right)\mathrm{is}12,\mathrm{which}\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}. \\ \mathrm{Median}=\frac{1}{2}\left\{\left(\frac{N}{2}\right)\mathrm{th}\mathrm{observation}+\left(\frac{N}{2}+1\right)\mathrm{th}\mathrm{observation}\right\} \\ =\left\{6\mathrm{th}\mathrm{observation}+7\mathrm{th}\mathrm{observation}\right\} \\ =\frac{1}{2}\left\{50+50\right\} \\ \mathrm{Median}=50 \\ \mathrm{Mean}=\frac{\sum \mathit{(}{f}_i\mathit{\times }{x}_i\mathit{)}}{\sum f_{\mathrm{i}}} \\ =\frac{612}{12} \\ \mathrm{Mean}=51 \\ \mathrm{Using}\mathrm{empirical}\mathrm{formula}: \\ \mathrm{Mode}=3\left(\mathrm{Median}\right)-2\left(\mathrm{Mean}\right) \\ =150-102 \\ \mathrm{Mode}=48 \end{gathered}$$

Hence, the median is 50, the mean is 51 and the mode is 48.