Central Tendency & DispersionMTP Dec 2023 Series IIQuestion 3064 of 473
All Questions

For a moderately skewed distribution, which of the following relationship is correct

Options

AMean −\displaystyle - Mode = 3\displaystyle 3 (Mean −\displaystyle - Median)
BMedian −\displaystyle - Mode = 3\displaystyle 3 (Mean −\displaystyle - Median)
CMean −\displaystyle - Median −3\displaystyle - 3 (Mean −\displaystyle - Mode)
DMean-Median = 3\displaystyle 3 (Median −\displaystyle - Mode).
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Correct Answer

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

All Options:

  • AMean −\displaystyle - Mode = 3\displaystyle 3 (Mean −\displaystyle - Median)
  • BMedian −\displaystyle - Mode = 3\displaystyle 3 (Mean −\displaystyle - Median)
  • CMean −\displaystyle - Median −3\displaystyle - 3 (Mean −\displaystyle - Mode)
  • DMean-Median = 3\displaystyle 3 (Median −\displaystyle - Mode).

Detailed Solution & Explanation

**Step 1: Recall the 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.** - **Option A:** Mean - Mode = 3(Mean - Median) ✓ This IS correct. - **Option B:** Median - Mode = 3(Mean - Median)? LHS = Median - Mode = Median - (3Median - 2Mean) = 2Mean - 2Median = 2(Mean - Median). RHS = 3(Mean - Median). LHS ≠ RHS → **Option B is incorrect**. **Correct answer is A.** Hence, **Option A** is the correct answer.

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