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Question
Find the Median of the following distribution:
| x | 3 | 5 | 10 | 12 | 8 | 15 |
| f | 2 | 4 | 6 | 10 | 8 | 7 |
Solution
Arranging the terms in ascending order and preparing the cumulative frequency table:
| x | f | c.f. |
| 3 | 2 | 2 |
| 5 | 4 | 6 |
| 8 | 8 | 14 |
| 10 | 6 | 20 |
| 12 | 10 | 30 |
| 15 | 7 | 37 |
Here, n = 37 which is odd.
So Median = `(("n" + 1)/2)^"th" "term"`
= `((37 + 1)/2)^"th" "term"`
= `(38/2)^"th"`
= 19th term
Hence, Median is the value of the 9th term = 10.
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