Question

Calculate the median for the following data.

Marks	20	9	25	50	40	80
Number of students	6	4	16	7	8	2

Answer 1

We will first arrange the given data in ascending order as follows:

Marks	Number of Students
9	4
20	6
25	16
40	8
50	7
80	2

Now, we will prepare the cumulative frequency table as follows:

Marks	Frequency	Cumulative Frequency
9	4	4
20	6	10
25	16	26
40	8	34
50	7	41
80	2	43

Here, n is 43, which is an odd number.
Thus, we have:
$\mathrm{Median}=\mathrm{Value}\mathrm{of}\left(\frac{n+1}{2}\right)\mathrm{th}\mathrm{observation}$
$$\begin{gathered} \mathrm{Median}\mathrm{marks}=\mathrm{Marks}\mathrm{obtained}\mathrm{by}\left(\frac{43+1}{2}\right)\mathrm{th}\mathrm{student} \\ =\mathrm{Marks}\mathrm{obtained}\mathrm{by}\mathrm{the}22\mathrm{nd}\mathrm{student} \\ \mathrm{Here},\mathrm{we}\mathrm{see}\mathrm{that}25\mathrm{marks}\mathrm{are}\mathrm{obtained}\mathrm{by}11\mathrm{th}\mathrm{to}26\mathrm{th}\mathrm{students}. \\ \mathrm{Marks}\mathrm{obtained}\mathrm{by}\mathrm{the}22\mathrm{nd}\mathrm{student}=25 \\ \mathrm{Median}\mathrm{marks}=25 \end{gathered}$$