Central Tendency & DispersionMTP Oct 21/ RTP Sep 24Question 3182 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 and 10 respectively., then the coefficient of variation of y\displaystyle y is

Options

A25
B30
C40
D20
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Correct Answer

✅ Option c — 40

All Options:

  • A25
  • B30
  • C40
  • D20

Detailed Solution & Explanation

**Given:** y=2x+5\displaystyle y = 2x + 5, SD(x)=5\displaystyle SD(x) = 5, xˉ=10\displaystyle \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 Mean of y\displaystyle y.** yˉ=2×10+5=25\bar{y} = 2 \times 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\% The correct mathematical answer is **40** (Option C). The given `correct_option` 'a' (25) is incorrect. Hence, **Option C** is the correct answer.

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