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

This question was previously asked in
SSC CGL JSO Tier-II, 2018 (Statistics) Official Paper-III (Held On: 14 Sept, 2019)
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  1. 32
  2. 64
  3. 22
  4. 16

Answer (Detailed Solution Below)

Option 2 : 64
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PYST 1: SSC CGL - English (Held On : 11 April 2022 Shift 1)
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Detailed Solution

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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

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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