Question

Calculate the median of the following distribution:

No. of goals	0	1	2	3	4	5
No. of matches	2	4	7	6	8	3

Answer 1

The given variates (no. of goals) are already in ascending order. We construct the cumulative frequency table as under:

Variate (No. of goals)	Frequency (No. of matches)	Cumulative frequency
0	2	2
1	4	6
2	7	13
3	6	19
4	8	27
5	3	30

Here, n = 30, which is even.
∴ Median
= ${\displaystyle \frac{\frac{\text{n}}{2}\text{th observation}+(\frac{\text{n}}{2}+1)\text{th observation}}{2}}$
= ${\displaystyle \frac{15\text{th observation}+16\text{th observation}}{2}}$
= ${\displaystyle \frac{3+3}{2}}$ = 3.
(∵ All observation form 14^th to 19^th are equal, each = 3).