Measures of Central Tendency and DispersionMCQPYQ June 19Question 3119 of 473
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If σ2=100\displaystyle \sigma^2 = 100 & coefficient of variation =20%\displaystyle = 20\% then x\displaystyle x

Options

A60\displaystyle 60
B70\displaystyle 70
C80\displaystyle 80
D50\displaystyle 50
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Correct Answer

✅ Option d — 50\displaystyle 50

All Options:

  • A60\displaystyle 60
  • B70\displaystyle 70
  • C80\displaystyle 80
  • D50\displaystyle 50

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Detailed Solution & Explanation

We are given: - Variance: σ2=100  ⟹  Standard Deviation (σ)=100=10\displaystyle \sigma^2 = 100 \implies \text{Standard Deviation } (\sigma) = \sqrt{100} = 10 - Coefficient of Variation (C.V.) = 20%\displaystyle 20\% The formula for the coefficient of variation is: C.V.=σxˉ×100C.V. = \frac{\sigma}{\bar{x}} \times 100 Substitute the given values: 20=10xˉ×10020 = \frac{10}{\bar{x}} \times 100 20xˉ=1000  ⟹  xˉ=5020\bar{x} = 1000 \implies \bar{x} = 50 Hence, **Option D** 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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