Central Tendency & DispersionMTP March 22Question 3061 of 473
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For moderately skewed distribution, the median is twice the mean, then mode is \_ times the median.

Options

A3\displaystyle 3
B2\displaystyle 2
C23\displaystyle \frac{2}{3}
D32\displaystyle \frac{3}{2}
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Correct Answer

✅ Option b — 2\displaystyle 2

All Options:

  • A3\displaystyle 3
  • B2\displaystyle 2
  • C23\displaystyle \frac{2}{3}
  • D32\displaystyle \frac{3}{2}

Detailed Solution & Explanation

**Step 1: Set up notation.** Let Mean = μ\displaystyle \mu, Median = 2μ\displaystyle 2\mu (given: median is twice mean). **Step 2: Apply the empirical formula.** Mode=3×Median−2×Mean=3(2μ)−2μ=6μ−2μ=4μ\text{Mode} = 3 \times \text{Median} - 2 \times \text{Mean} = 3(2\mu) - 2\mu = 6\mu - 2\mu = 4\mu **Step 3: Compute Mode/Median ratio.** ModeMedian=4μ2μ=2\frac{\text{Mode}}{\text{Median}} = \frac{4\mu}{2\mu} = 2 Mode = 2×\displaystyle 2 \times Median. Hence, **Option B** is the correct answer.

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