Central Tendency & DispersionMTP Nov 18Question 3049 of 473
All Questions

The relationship between AM, GM, and Median

Options

AMean-Mode = 3(Mean-Median)
BMode = 2 Median - 3 Median
CMedian- Mode = 3 (Median-mean)
Dnone of these
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Correct Answer

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

All Options:

  • AMean-Mode = 3(Mean-Median)
  • BMode = 2 Median - 3 Median
  • CMedian- Mode = 3 (Median-mean)
  • Dnone of these

Detailed Solution & Explanation

**Step 1: Recall the empirical formula.** Karl Pearson's empirical relationship: Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} **Step 2: Evaluate options.** - Option A: Mean - Mode = 3(Mean - Median) — this is a correct rearrangement of the formula. ✓ - Option B: Mode = 2 Median - 3 Median = -1 × Median — this is obviously wrong mathematically. - Option C: Median - Mode = 3(Median - Mean) — let's verify: LHS = Median - (3Median - 2Mean) = 2Mean - 2Median = 2(Mean - Median). RHS = 3(Median - Mean) = -3(Mean - Median). These are not equal. **Step 3: Correct answer.** Option A states the correct relationship: Mean - Mode = 3(Mean - Median). Note: The exam key says B, but Option B is mathematically meaningless. The correct answer is **A**. Hence, **Option A** is the correct answer.

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