If the data is not following a symmetrical distribution, then the relationship between mean, median and mode is:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → Mode = 3 Median - 2 Mean
In a symmetrical distribution the mean, median and mode are equal. When the distribution is not symmetrical (moderately skewed), they separate, and the empirical relation found by Karl Pearson links them:
Mode \(=3\) Median \(-\,2\) Mean
It is the same as saying that the median lies between the mean and the mode, one-third of the way from the mean: Mean − Mode \(=3\)(Mean − Median).
Why the other options are incorrect
Option (1) Median = 3 Mode - 2 Mean — Incorrect. It swaps the places of the median and the mode in the relation.
Option (2) Mode = 2 Median - 3 Mean — Incorrect. The coefficients 3 and 2 are interchanged; with all three equal it would give Mode \(=-\)Mean.
Option (3) Mode = Median = Mean — Incorrect. This holds only for a symmetrical distribution, which the question rules out.