Central Tendency & DispersionICAI SM, MTP May 19 Series IIQuestion 3159 of 473
All Questions

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\displaystyle 10 respectively, then the coefficient of variation of y\displaystyle y is

Options

A25\displaystyle 25
B30\displaystyle 30
C40\displaystyle 40
D20\displaystyle 20
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Correct Answer

✅ Option c — 40\displaystyle 40

All Options:

  • A25\displaystyle 25
  • B30\displaystyle 30
  • C40\displaystyle 40
  • D20\displaystyle 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) = \bar{x} = 10 **Step 1: Find SD of y\displaystyle y.** SD(y)=∣2∣×SD(x)=2×5=10SD(y) = |2| \times SD(x) = 2 \times 5 = 10 **Step 2: Find AM of y\displaystyle y.** yˉ=2xˉ+5=2(10)+5=25\bar{y} = 2\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) = \frac{SD(y)}{\bar{y}} \times 100 = \frac{10}{25} \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 \times 5 = 10; yˉ=2(10)+5=25\displaystyle \bar{y} = 2(10)+5 = 25; CV=10/25×100=40\displaystyle CV = 10/25 \times 100 = 40. So Option C (40) is mathematically correct. Hence, **Option C** is the correct answer.

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