Question

Find the median for the following frequency distribution.

Variate	17	20	22	15	30	25
Frequency	5	9	4	3	10	6

Answer 1

First, we will arrange the following data in ascending order.

Variate	Frequency
15	3
17	5
20	9
22	4
25	6
30	10

Now, based on this data, we will make a cumulative frequency table

Variate	Frequency	Cumulative Frequency
15	3	3
17	5	8
20	9	17
22	4	21
25	6	27
30	10	37

Here, n =37, which is odd.

$\mathrm{Median}=\mathrm{value}\mathrm{of}\left(\frac{n+1}{2}\right)\mathrm{th}\mathrm{observation}$
$$\begin{gathered} \mathrm{Therefore},\mathrm{median}=\mathrm{value}\mathrm{of}\left(\frac{37+1}{2}\right)\mathrm{th}\mathrm{observation} \\ =\mathrm{value}\mathrm{of}19\mathrm{th}\mathrm{observation} \\ \mathrm{Here},\mathrm{we}\mathrm{see}\mathrm{that}\text{the}\mathrm{value}\mathrm{of}18\mathrm{th}\mathrm{to}21\mathrm{th}\mathrm{observation}\mathrm{is}22. \\ \mathrm{Therefore},\mathrm{value}\mathrm{of}\text{the}19\mathrm{th}\mathrm{observation}\mathrm{is}22. \\ \mathrm{Hence},\mathrm{median}\mathrm{for}\mathrm{the}\text{given}\mathrm{data}\mathrm{is}22. \end{gathered}$$