Measures of Central Tendency and DispersionMCQMTP Nov 18Question 3049 of 473
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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

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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.

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.

Key Concepts to Understand

Median

The middle value of a data set when arranged in ascending or descending order. It divides the distribution into two equal halves. For even n: Median = average of (n/2)th and (n/2 + 1)th values. It is NOT affected by extreme values.

Related Comparison Tables

Mean vs Median vs Mode: Measures of Central TendencyFiscal Policy vs Monetary Policy: CA Foundation Economics

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