Question

The points scored by a kabaddi team in a series of matches are as follows:
8, 24, 10, 14, 5, 15, 7, 2, 17, 27, 10, 7, 48, 8, 18, 28.
Find the median of the points scored by the team.

Answer 1

Arranging the scores in ascending order, we have:
2, 5, 7, 7, 8, 8, 10, 10, 14, 15, 17, 18, 24, 28, 48

$$\begin{gathered} \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{observations}\mathrm{is}16,\mathrm{which}\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{Median}=\frac{1}{2}\left[{\frac{\mathrm{n}}{2}}^{\mathrm{th}}\mathrm{term}+{\left(\frac{\mathrm{n}}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[{\frac{16}{2}}^{\mathrm{th}}\mathrm{term}+{\left(\frac{16}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[8^{\mathrm{th}}\mathrm{term}+{\left(9\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[10+14\right] \\ =\frac{1}{2}\times 24 \\ =12 \end{gathered}$$