Central Tendency & DispersionMTP May 19 Series IIQuestion 3053 of 473
All Questions

For a moderately skewed distribution, which of the following relationship holds?

Options

AMean - Mode = 3 (Mean - Median)
BMean - Mode = 3 (Mean - Median)
CMean - Median = 3 (Mean - Mode)
DMean - Median = 3 (Median - Mode)
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Correct Answer

✅ Option a — Mean - Mode = 3 (Mean - Median)

All Options:

  • AMean - Mode = 3 (Mean - Median)
  • BMean - Mode = 3 (Mean - Median)
  • CMean - Median = 3 (Mean - Mode)
  • DMean - Median = 3 (Median - Mode)

Detailed Solution & Explanation

**Step 1: Apply Karl Pearson's empirical formula.** Mode=3Median−2Mean\text{Mode} = 3\text{Median} - 2\text{Mean} ⇒Mean−Mode=3(Mean−Median)\Rightarrow \text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median}) **Step 2: Evaluate each option.** - Options A and B state: Mean - Mode = 3(Mean - Median) — this is correct. - Option C: Mean - Median = 3(Mean - Mode) — from the formula: Mean - Median = (Mean - Mode)/3, so this is **wrong** (it would mean Mean - Median = 3(Mean - Mode) only if Mean - Mode = (1/9)(Mean - Mode), which is impossible unless Mean = Mode). **Correct formula:** Mean - Mode = 3(Mean - Median) = **Options A/B**. Hence, **Option A** is the correct answer.

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