Measures of Central Tendency and DispersionMCQICAI SM, MTP May 19 Series IIQuestion 3159 of 473
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If x\displaystyle x and y\displaystyle y are related by y=2x+5\displaystyle y = 2x + 5 and the SD and AM of x\displaystyle x are known to be 5\displaystyle 5 and $10$ respectively, then the coefficient of variation of $y$ is

Select Your Answer (Keyboard: A, B, C, D)
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Correct Answer

✅ Option c — $40$

All Options:

  • A$25$
  • B$30$
  • C$40$
  • D$20$

Detailed Solution & Explanation

**Given:** y=2x+5\displaystyle y = 2x + 5, SD(x)=5\displaystyle SD(x) = 5, AM(x)=xˉ=10\displaystyle AM(x) = xˉ=10\displaystyle \bar{x} = 10 **Step 1: Find SD of y\displaystyle y.** SD(y)=∣2∣×SD(x)=2×5=10SD(y) = |2| ×\displaystyle \times SD(x) = 2 ×\displaystyle \times 5 = 10 **Step 2: Find AM of y\displaystyle y.** yˉ=2xˉ+5=2(10)+5=25yˉ=2\displaystyle \bar{y} = 2xˉ+5=2\displaystyle \bar{x} + 5 = 2(10) + 5 = 25 **Step 3: Calculate CV of y\displaystyle y.** CV(y)=SD(y)yˉ×100=1025×100=40%CV(y) = SD(y)yˉ\displaystyle \frac{SD(y)}{\bar{y}} ×\displaystyle \times 100 = 1025\displaystyle \frac{10}{25} ×\displaystyle \times 100 = 40\% Wait — the answer is 40%, which is Option C. But the given `correct_option` is 'a' (25). Let me double-check: SD(y)=2×5=10\displaystyle SD(y) = 2 ×\displaystyle \times 5 = 10; yˉ=2(10)+5=25\displaystyle yˉ=2\displaystyle \bar{y} = 2(10)+5 = 25; CV=10/25×100=40\displaystyle CV = 10/25 ×\displaystyle \times 100 = 40. So Option C (40) is mathematically correct. Hence, **Option C** 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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