Mathematics
Find the mode and the 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
| x | f | Cumulative frequency |
|---|---|---|
| 10 | 1 | 1 |
| 11 | 4 | 5 (1 + 4) |
| 12 | 7 | 12 (5 + 7) |
| 13 | 5 | 17 (12 + 5) |
| 14 | 9 | 26 (17 + 9) |
| 15 | 3 | 29 (26 + 3) |
From table,
14 has the highest frequency.
∴ Mode = 14.
Here, n = 29, which is odd.
Median = th term
= = 15th term.
From table,
13th to 17th term = 13.
Median = 13.
Hence, median = 13 and mode = 14.
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