Question

Which relationship is true for Mean, Median and Mode?

• A. Mean - Mode = 3 (Mean - Median)
• B. Mean - Mode = 3 (Mean + Median)
• C. Mean - Mode = 3 (Mode - Median)
• D. None of these

Hint:

The relation Mean - Mode = 3(Mean - Median) is an empirical formula, not always exact.

Answer 1

The Correct Option is A

Step 1: Recall empirical relation.
Karl Pearson’s empirical formula:
\[ \text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} \]
Step 2: Rearrange.
\(\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median})\).