Central Tendency & DispersionMTP Apr 21Question 3175 of 473
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The Sum of the squares of the deviations from mean of 10 observations is 250. Mean of the data is 10. Find coefficient of variation.

Options

A10%
B25%
C50%
D0%
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Correct Answer

✅ Option c — 50%

All Options:

  • A10%
  • B25%
  • C50%
  • D0%

Detailed Solution & Explanation

**Given:** ∑(xi−xˉ)2=250\displaystyle \sum(x_i - \bar{x})^2 = 250, n=10\displaystyle n = 10, xˉ=10\displaystyle \bar{x} = 10 **Step 1: Calculate Variance.** σ2=25010=25\sigma^2 = \frac{250}{10} = 25 **Step 2: Calculate SD.** σ=25=5\sigma = \sqrt{25} = 5 **Step 3: Calculate CV.** CV=σxˉ×100=510×100=50%CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{5}{10} \times 100 = 50\% So CV = 50% (Option C). The given `correct_option` 'a' (10%) is incorrect. Hence, **Option C** is the correct answer.

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