Question

Find the median for the following data.

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

Answer 1

We will first arrange the given data in ascending order.

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

Now, we will prepare a cumulative frequency table.

Variate	Frequency	Cumulative Frequency
16	9	9
18	8	17
20	13	30
23	4	34
25	4	38
26	6	44
28	11	55
30	5	60

Here, n is 60, which is an even number.
Now,
$\mathrm{Median}=\mathrm{Mean}\mathrm{of}\left(\frac{n}{2}\right)\mathrm{th}\&\left(\frac{n}{2}+1\right)\mathrm{th}\mathrm{observations}$
$$\begin{gathered} \mathrm{Median}=\mathrm{Mean}\mathrm{of}\left(\frac{60}{2}\right)\mathrm{th}\&\left(\frac{60}{2}+1\right)\mathrm{th}\mathrm{observations} \\ =\mathrm{Mean}\mathrm{of}30\mathrm{th}\&31\mathrm{st}\mathrm{observations} \\ \mathrm{Value}\mathrm{of}\mathrm{the}30\mathrm{th}\mathrm{observation}\mathrm{is}20\&\mathrm{value}\mathrm{of}31\mathrm{st}\mathrm{to}34\mathrm{th}\mathrm{observations}\mathrm{is}23. \\ \therefore \mathrm{Median}=\frac{1}{2}\left(20+23\right)=21.5 \end{gathered}$$