# If Arithmetic mean and coefficient of variation of x are 10 and 40 respectively, then the variance of y = 10 - 2x is:

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If Arithmetic mean and coefficient of variation of x are 10 and 40 respectively, then the variance of y = 10 - 2x is:
1. 32
2. 64
3. 22
4. 16

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Correct Answer - Option 2 : 64

Given

Arithmetic mean =  (μ) = 10

Coefficient of variation = CV = 40% or 0.4

Formula

CV = σ/μ

σ = Standard deviation

μ = Mean

Calculation

0.4 = σ/10

⇒ σ/ = Standard deviation = 0.4 × 10 = 4

Now, Variance= V = (standard deviation)2 = σ2

⇒ Variance = 42 = 16

We know that V(ax + b) = a2(V(x)

⇒ V(10 - 2x) = (-2)V(X)

⇒  V(10 - 2x) = 4V(x)

∴ V(10 - 2x) = 4 × 16 = 64

Symbol of Standard deviation = σ

Variance = square of standard deviation = σ2

Coefficient of variation = CV = CV = σ/μ

μ = Population mean