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
= `("n"/2 "th observation" + ("n"/2 + 1)"th observation")/(2)`
= `(15"th observation" + 16"th observation")/(2)`
= `(3 + 3)/(2)` = 3.
(∵ All observation form 14^th to 19^th are equal, each = 3).