Central Tendency & DispersionPYQ Dec 23Question 3042 of 473
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If the mean and median of a moderately asymmetrical series are 26.8 and 27.9 respectively, then the most probable mode is:

Options

A30.1
B30.4
C34.3
D70.8
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Correct Answer

✅ Option a — 30.1

All Options:

  • A30.1
  • B30.4
  • C34.3
  • D70.8

Detailed Solution & Explanation

**Step 1: Apply the empirical formula.** Mode=3×Median−2×Mean\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} **Step 2: Substitute values.** - Mean = 26.8, Median = 27.9 Mode=3×27.9−2×26.8\text{Mode} = 3 \times 27.9 - 2 \times 26.8 =83.7−53.6=30.1= 83.7 - 53.6 = 30.1 The Mode = 30.1\displaystyle 30.1 = **Option A**. Note: The exam key says B (30.4\displaystyle 30.4), but the calculation gives 30.1\displaystyle 30.1 (Option A). Hence, **Option A** is the correct answer.

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