Central Tendency & DispersionPYQ Dec 22Question 3137 of 473
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If the coefficient of variation and standard deviation are 30 and 12 respectively, then the arithmetic mean of the distribution is:

Options

A40\displaystyle 40
B36\displaystyle 36
C25\displaystyle 25
D19\displaystyle 19
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Correct Answer

✅ Option a — 40\displaystyle 40

All Options:

  • A40\displaystyle 40
  • B36\displaystyle 36
  • C25\displaystyle 25
  • D19\displaystyle 19

Detailed Solution & Explanation

**Given:** CV = 30, SD (σ\displaystyle \sigma) = 12 **Step 1: Use the formula for CV.** CV=σxˉ×100CV = \frac{\sigma}{\bar{x}} \times 100 **Step 2: Substitute and solve for xˉ\displaystyle \bar{x}.** 30=12xˉ×10030 = \frac{12}{\bar{x}} \times 100 xˉ=12×10030=120030=40\bar{x} = \frac{12 \times 100}{30} = \frac{1200}{30} = 40 **Result:** Arithmetic Mean = 40 Hence, **Option A** is the correct answer.

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