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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 |
Solution
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 14th to 19th are equal, each = 3).
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