Measures of Central Tendency and DispersionMCQMTP 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)

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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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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