Mathematics
Find the mode and median of the following frequency distribution :
| x | f |
|---|---|
| 10 | 1 |
| 11 | 4 |
| 12 | 7 |
| 13 | 5 |
| 14 | 9 |
| 15 | 3 |
Measures of Central Tendency
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Answer
The variates are already in ascending order. We construct the cumulative frequency table as under :
| x | f | Cumulative frequency (C.F.) |
|---|---|---|
| 10 | 1 | 1 |
| 11 | 4 | 5 |
| 12 | 7 | 12 |
| 13 | 5 | 17 |
| 14 | 9 | 26 |
| 15 | 3 | 29 |
Total number of observations = 29, which is odd.
All observations from 13th to 17th are equal, each = 13, so median = 13.
As the variate 14 has maximum frequency 9, so mode = 14.
Hence, median = 13 and mode = 14.
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