Calculate the median for the following frequency distribution :

Variate	Frequency
3	3
6	4
10	2
12	8
7	13
15	10

By rearranging the variates in the ascending order along with their frequencies, we construct the cumulative frequency as under

Total number of observations = 40, which is even.

By formula,

$\Rightarrow \text{Median} = \dfrac{\left(\dfrac{n}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{n}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\left(\dfrac{40}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{40}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{20th term} + \text{21st term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{7} + \text{10}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{17}}{2} \\[1em]$

∴ Median = 8.5.

Hence, median is 8.5.