Central Tendency & DispersionPYQ June 19Question 3028 of 473
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For a symmetric distribution

Options

AMean = Median = Mode
BMode = 3\displaystyle 3 Median = 2\displaystyle 2 Mean
CMode = 13\displaystyle \frac{1}{3} Median = 12\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 = 3\displaystyle 3 Median = 2\displaystyle 2 Mean
  • CMode = 13\displaystyle \frac{1}{3} Median = 12\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: Mean=Median=Mode\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.

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