Measures of Central Tendency and DispersionMCQPYQ May 18Question 3025 of 473
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Relation between mean, median and mode is

Options

Amean - mode = 3\displaystyle 3 (mean - median)
Bmean - median = 3\displaystyle 3 (mean - mode)
Cmean - median = 2\displaystyle 2 (mean - mode)
Dmean - mode = 3\displaystyle 3 (mean - median)
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Correct Answer

✅ Option a — mean - mode = 3\displaystyle 3 (mean - median)

All Options:

  • Amean - mode = 3\displaystyle 3 (mean - median)
  • Bmean - median = 3\displaystyle 3 (mean - mode)
  • Cmean - median = 2\displaystyle 2 (mean - mode)
  • Dmean - mode = 3\displaystyle 3 (mean - median)

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Detailed Solution & Explanation

**Step 1: Recall the empirical relationship between mean, median, and mode.** For a moderately skewed distribution, Karl Pearson's empirical formula states: Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} **Step 2: Rearrange to find the relation.** Rearranging: Mean−Mode=Mean−(3Median−2Mean)=3Mean−3Median=3(Mean−Median)\text{Mean} - \text{Mode} = \text{Mean} - (3\text{Median} - 2\text{Mean}) = 3\text{Mean} - 3\text{Median} = 3(\text{Mean} - \text{Median}) So the standard relation is: Mean−Mode=3(Mean−Median)\text{Mean} - \text{Mode} = 3(\text{Mean} - \text{Median}) **Step 3: Check options.** - Option A and D are identical and state: Mean - Mode = 3(Mean - Median) — this is the correct standard formula. - Option C states: Mean - Median = 2(Mean - Mode) — let's verify: From Mean - Mode = 3(Mean - Median): Mean - Median = (Mean - Mode)/3 ≠ 2(Mean - Mode) **Correct formula: Mean - Mode = 3(Mean - Median).** This matches **Options A and D** (they appear to be identical in text). 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.

Mode

The value that appears most frequently in a data set. A data set can be unimodal (one mode), bimodal (two modes), or multimodal (more than two modes). It is the only measure of central tendency applicable to qualitative (categorical) data.

Related Comparison Tables

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

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