Find out the median of the following frequency distribution:
| Variable | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | Total |
| Frequency | 5 | 7 | 11 | 9 | 8 | 7 | 3 | 5 | 55 |
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 14
The median is the middle value when all the observations are arranged in order. For \(N\) observations (\(N\) odd) it is the \(\left(\frac{N+1}{2}\right)\)th value, which the cumulative frequencies locate.
\(N=55\), so the median is the \(\frac{55+1}{2}=28\)th value
Cumulative frequencies: 11 → 5, 12 → 12, 13 → 23, 14 → 32, and so on
The values up to 13 cover the first 23 observations; the 24th to the 32nd are all 14
The 28th value is therefore 14, so median \(=14\)
Tip: 13 in Option (1) is the mode (the value with the highest frequency, 11), not the median.