Find the median for the following data :

Variate	Frequency
23	4
26	6
20	13
30	5
28	11
25	4
18	8
16	9

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

Total number of observations = 60, which is even.

By formula,

$\Rightarrow \text{Median} = \dfrac{\left(\dfrac{n}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{n}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\left(\dfrac{60}{2}\right)^{\text{th}} \text{term} + \left(\dfrac{60}{2} + 1\right)^{\text{th}} \text{term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{30th term} + \text{31st term}}{2} \\[1em] \Rightarrow \text{Median} = \dfrac{\text{20} + \text{23}}{2} \\[1em] \Rightarrow\text{Median} = \dfrac{\text{43}}{2} \\[1em]$

∴ Median = 21.5.

Hence, median is 21.5.