Question

Find the median of the following frequency distribution:

Variate	3	6	10	12	7	15
Frequency	3	4	2	8	12	10

Answer 1

The following table is in ascending order:

Variate	Frequency	Cumulative Frequency
3	3	3
6	4	7
7	13	20
10	2	22
12	8	30
15	10	40
	n = 40

$$\begin{gathered} \mathrm{The}\mathrm{number}\mathrm{of}\mathrm{observations}\mathrm{is}40,\mathrm{which}\mathrm{is}\mathrm{an}\mathrm{even}\mathrm{number}. \\ \mathrm{Thus},\mathrm{we}\mathrm{have}: \\ \mathrm{Median}=\frac{1}{2}\left[{\left(\frac{\mathrm{n}}{2}\right)}^{\mathrm{th}}\mathrm{term}+{\left(\frac{\mathrm{n}}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[{\left(\frac{40}{2}\right)}^{\mathrm{th}}\mathrm{term}+{\left(\frac{40}{2}+1\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[{20}^{\mathrm{th}}\mathrm{term}+{\left(21\right)}^{\mathrm{th}}\mathrm{term}\right] \\ =\frac{1}{2}\left[7+10\right] \\ =8.5 \end{gathered}$$