Measures of Central Tendency and DispersionMCQMTP Nov 19Question 3163 of 473
All Questions

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

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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.

About This Chapter: Measures of Central Tendency and Dispersion

Paper

Paper 3: Quantitative Aptitude

Weightage

12-15 Marks

Key Topics

Mean, Median, Mode, Range, Mean Deviation, Standard Deviation

The core foundation of Statistics. This chapter covers Mean (Arithmetic, Geometric, Harmonic), Median, Mode, and their properties. It also explores measures of spread like Range, Mean Deviation, Standard Deviation, and Quartile Deviation.

View Official ICAI Syllabus

Exam Strategy Tip

Do not just memorize formulas; ICAI loves asking about the mathematical properties (e.g., 'sum of deviations from the AM is always zero'). You can usually eliminate 2 options just by knowing the properties.

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