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Question
Calculate the median of the following distribution:
| Weight (in nearest kg.) | No. of students |
| 46 | 7 |
| 48 | 5 |
| 50 | 8 |
| 52 | 12 |
| 53 | 10 |
| 54 | 2 |
| 55 | 1 |
Solution
The given variates (weights of students) are already in ascending order. We construct the cumulative frequency table as under:
| Variable (weight) |
Frequency (No.of Students) |
Cumulative frequency |
| 46 | 7 | 7 |
| 48 | 5 | 12 |
| 50 | 8 | 20 |
| 52 | 12 | 32 |
| 53 | 10 | 42 |
| 54 | 2 | 44 |
| 55 | 1 | 45 |
Here, n = 45, which is odd.
∴ Median = `("n" + 1)/(2)`th observation
= 23rd observation = 52.
(∵ All observation from 21st to 32nd are equal, each = 52).
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