Central Tendency & DispersionMTP Nov 19Question 3163 of 473
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Find the coefficient of variation if the sum of squared deviations taken from mean 40\displaystyle 40 of 10\displaystyle 10 observations is 360\displaystyle 360.

Options

A15\displaystyle 15
B20\displaystyle 20
C40\displaystyle 40
DNone of these
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Correct Answer

✅ Option a — 15\displaystyle 15

All Options:

  • A15\displaystyle 15
  • B20\displaystyle 20
  • C40\displaystyle 40
  • DNone of these

Detailed Solution & Explanation

**Given:** Mean xˉ=40\displaystyle \bar{x} = 40, n=10\displaystyle n = 10, ∑(xi−xˉ)2=360\displaystyle \sum(x_i - \bar{x})^2 = 360 **Step 1: Calculate Variance.** σ2=∑(xi−xˉ)2n=36010=36\sigma^2 = \frac{\sum(x_i - \bar{x})^2}{n} = \frac{360}{10} = 36 **Step 2: Calculate SD.** σ=36=6\sigma = \sqrt{36} = 6 **Step 3: Calculate CV.** CV=σxˉ×100=640×100=15%CV = \frac{\sigma}{\bar{x}} \times 100 = \frac{6}{40} \times 100 = 15\% So CV = 15%, which is Option A. The given `correct_option` 'd' (None of these) is incorrect since Option A (15) is the correct answer. Hence, **Option A** is the correct answer.

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