Question

The following table gives the marks obtained by 65 students in statistics in a certain examination . Calculate the median.

Marks	No of Students
More than 70	8
More than 60	18
More than 50	40
More than 40	45
More than 30	50
More than 20	63
More than 10	65

Answer 1

Marks	Students c.f
More than 70 More than 60 More than 50 More than 40 More than 30 More than 20 More than 10	8 18 40 45 50 63 65

Now the more than cumulative frequency distribution can be converted into class intervals as follows.

C.I.	f	c.f
10 – 20	2	2
20 – 30	13	15
30 – 40	5	20
40 – 50	5	25
50 – 60	22	47
60 – 70	10	57
70 and above	8	65
	Ʃf = 65

Median class is given by the size of the ${\left(\frac{N}{2}\right)}^{\mathrm{th}}$ item, i.e. the ${\left(\frac{65}{2}\right)}^{\mathrm{th}}$ item, which is the 32.5^th item. This corresponds to the class interval 50−60, so this is the median class.

$$\begin{gathered} M=l_1+\frac{\left({\displaystyle \frac{N}{2}}\right)-c.f}{f}\times i \\ =50+\frac{32.5-25}{22}\times 10 \\ =50+\frac{75}{22}=50+3.4 \\ =53.4 \end{gathered}$$
Thus, the median marks is 53.4.