Which of the following is/are incorrect?
A. 3 Median - Mean = 2 Mode
B. 3 Median - 2 Mean = Mode
C. 3 Mode - 2 Mean = Median
D. 3 Mean - 2 Median = Mode
E. 3 Mean - Median = 2 Mode
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → A, C, D and E only
For a moderately skewed distribution, the empirical relation between the three averages is Mode = 3 Median − 2 Mean. A statement is correct only if it is this relation or a rearrangement of it.
A. 3 Median - Mean = 2 Mode Incorrect. Doubling the relation gives 2 Mode = 6 Median − 4 Mean, not 3 Median − Mean.
B. 3 Median - 2 Mean = Mode Correct. This is the empirical relation itself.
C. 3 Mode - 2 Mean = Median Incorrect. Mode and median have changed places; the 3 goes with the median, not the mode.
D. 3 Mean - 2 Median = Mode Incorrect. Mean and median have changed places; the relation gives Mode = 3 Median − 2 Mean.
E. 3 Mean - Median = 2 Mode Incorrect. From the relation, 2 Mode = 6 Median − 4 Mean, so the 3 goes with the median, not the mean.