Central Tendency & DispersionMTP May 19Question 3051 of 473
All Questions

For a moderately skewed distribution, which is true

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: Recall the empirical formula.** Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} **Step 2: Rearrange to standard form.** Mean−Mode=3Mean−3Median=3(Mean−Median)\text{Mean} - \text{Mode} = 3\text{Mean} - 3\text{Median} = 3(\text{Mean} - \text{Median}) This matches Options A and B (which appear identical): **Mean - Mode = 3(Mean - Median)**. **Step 3: Check option D.** Mean - Median = 3(Median - Mode)? Let's verify: From the formula, Mean - Mode = 3(Mean - Median) → Mean - Median = (Mean - Mode)/3 And 3(Median - Mode) = 3 × (Median - Mode) — this requires additional verification. Substituting Mode = 3Median - 2Mean: Median - Mode = Median - 3Median + 2Mean = 2Mean - 2Median = 2(Mean - Median) So 3(Median - Mode) = 6(Mean - Median) ≠ (Mean - Median). **Correct formula is A/B.** The mathematically verified answer is **Mean - Mode = 3(Mean - Median)**. Hence, **Option A** is the correct answer.

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