If L, N and M denote the mode, median and mean of a data set respectively,…
2026
If L, N and M denote the mode, median and mean of a data set respectively, which of the following relations is correct?
- A.
L=2N−3M
- B.
L=2M−3N
- C.
L=3N−2M
- D.
L=5N−3M
Attempted by 3 students.
Show answer & explanation
Correct answer: C
Concept: For a moderately skewed frequency distribution, the three measures of central tendency — mean, median and mode — are related by Karl Pearson's empirical formula: Mean − Mode ≈ 3 × (Mean − Median).
Applying this to the question:
Let L = mode, N = median and M = mean, as given in the question.
Start from the empirical relation: M − L = 3(M − N).
Expand the right-hand side: M − L = 3M − 3N.
Rearrange to isolate L: L = M − 3M + 3N = 3N − 2M.
Cross-check: in a perfectly symmetric distribution, mode, median and mean coincide, i.e., L = N = M. Substituting into L = 3N − 2M gives L = 3M − 2M = M, which equals L as required — confirming the relation holds consistently.
Result: L = 3N − 2M.