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Question
Find the mode and the median of the following frequency distribution:
| x | 10 | 11 | 12 | 13 | 14 | 15 |
| f | 1 | 4 | 7 | 5 | 9 | 3 |
Solution
| x | f | cf |
| 10 | 1 | 1 |
| 11 | 4 | 5 |
| 12 | 7 | 12 |
| 13 | 5 | 17 |
| 14 | 9 | 26 |
| 15 | 3 | 29 |
| N = 29 |
Here `N = 29 => N/2 = 29/2 = 14.5`
We find that the cf just greater than `N/2 = 14.5` is 17 and the value of x corresponding to 17 is 13.
Therefore, Median = 13
To find mode: From the table, it is clear that the value 14 has maximum frequency 9.
Hence, the mode of the data is 14.
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