Question
Download Solution PDFIf Arithmetic mean and coefficient of variation of x are 10 and 40 respectively, then the variance of y = 10 - 2x is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven
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)2 V(X)
⇒ V(10 - 2x) = 4V(x)
∴ V(10 - 2x) = 4 × 16 = 64
Important Points
Symbol of Standard deviation = σ
Variance = square of standard deviation = σ2
Coefficient of variation = CV = CV = σ/μ
μ = Population mean
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