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Question
Obtain the median for the following frequency distribution:
| x : | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| f : | 8 | 10 | 11 | 16 | 20 | 25 | 15 | 9 | 6 |
Solution
Calculation of Median
| x | f | c.f. |
| 1 | 8 | 8 |
| 2 | 10 | 18 |
| 3 | 11 | 29 |
| 4 | 16 | 45 |
| 5 | 20 | 65 |
| 6 | 25 | 90 |
| 7 | 15 | 105 |
| 8 | 9 | 114 |
| 9 | 6 | 120 |
| N = 120 |
Here, N = 120, so, `"N"/(2)` = 60.
The cumulative frequency just greater than `"N"/(2)` i.e., 60 is 65. The value of the variate corresponding to 65 is 5.
Hence, median = 5.
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