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Question
Find the mode and the median of the following frequency distributions.
| x | 10 | 11 | 12 | 13 | 14 | 15 |
| f | 1 | 4 | 7 | 5 | 9 | 3 |
Solution
Since the frequency for x = 14 is maximum.
So mode = 14.
| x | f | Cumlative Frequency |
| 10 | 1 | 1 |
| 11 | 4 | 5 |
| 12 | 7 | 12 |
| 13 | 5 | 17 |
| 14 | 9 | 26 |
| 15 | 3 | 29 |
| N=29 |
Median=`((n+1)/2)^("th")` term
= `(30/2)^("th")` term
= `15^("th")` term
Frequency of the `15^"th"` term
According to the table it can be observed that the value of x from to the `13^"th"` term to the `17^"th"` term is 13.
So the median = 13.
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