Measures of Central Tendency and DispersionMCQPYQ June 19Question 3028 of 473

For a symmetric distribution

Options

AMean = Median = Mode

BMode =

\displaystyle 3

Median =

\displaystyle 2

Mean

CMode =

\displaystyle \frac{1}{3}

Median =

\displaystyle \frac{1}{2}

Mean

DNone of these

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Correct Answer

✅ Option a — Mean = Median = Mode

All Options:

AMean = Median = Mode
BMode = $\displaystyle 3$ Median = $\displaystyle 2$ Mean
CMode = $\displaystyle \frac{1}{3}$ Median = $\displaystyle \frac{1}{2}$ Mean
DNone of these

Detailed Solution & Explanation

**Step 1: Recall the property of a symmetric distribution.** For a **perfectly symmetric** distribution (like a normal distribution), there is no skewness. The mean, median, and mode coincide:

\text{Mean} = \text{Median} = \text{Mode}

**Step 2: Evaluate options.** - **Option A**: Mean = Median = Mode — this is exactly the property of symmetric distribution. ✓ - **Option B**: Mode = 3 Median = 2 Mean — this would mean all are not equal, which contradicts symmetry. - **Option C**: Mode = (1/3) Median = (1/2) Mean — also contradicts symmetry. **Conclusion:** For a symmetric distribution, Mean = Median = Mode = **Option A**. Note: The exam key says C, which is incorrect mathematically. 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.

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