For a set of data, the mean is 18.5 and the median is 22. Using the empirical relation between mean, median and mode, what is the mode?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 29
For a moderately skewed set of data, the empirical relation is Mode \(=3\times\) Median \(-\,2\times\) Mean.
Mode \(=3\times22-2\times18.5\)
\(=66-37=29\)
The mode is 29.
Why the other options are incorrect
Option (1) 103 — Incorrect. This adds 2 × mean instead of subtracting it.
Option (3) 25.5 — Incorrect. This uses 2 × median − mean; the relation is 3 × median − 2 × mean.
Option (4) 11.5 — Incorrect. This swaps the mean and the median in the relation.