What is empirical relationship between mean, median and mode?
A. Mean - Mode = 3(Mean - Median)
B. Mode = Mean - Median
C. Mode = 3 Median - 2 Mean
D. Median - Mode = 3 (Mean - Median)
E. Mode = 2 Mean + 3 Median
Choose the correct answer from the options given below.
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Both A and C only
For a moderately skewed distribution, Karl Pearson’s empirical relationship is Mode = 3 Median − 2 Mean. Each statement is compared with it.
A. Mean - Mode = 3(Mean - Median) Correct. Putting Mode = 3 Median − 2 Mean on the left gives Mean − 3 Median + 2 Mean = 3 Mean − 3 Median, which is 3(Mean − Median); this is the same relationship written another way.
B. Mode = Mean - Median Incorrect. It drops the factors 3 and 2; for a symmetric distribution, where all three are equal, it would wrongly give Mode = 0.
C. Mode = 3 Median - 2 Mean Correct. This is the standard form of the empirical relationship.
D. Median - Mode = 3 (Mean - Median) Incorrect. The correct form gives Median − Mode = 2(Mean − Median), not 3 times.
E. Mode = 2 Mean + 3 Median Incorrect. The signs and factors are swapped: the mean is subtracted, and the median carries the 3; for equal values it would give Mode = 5 Mean.