यदि x के विचरण का अंकगणित औसत और गुणांक क्रमशः 10 और 40 हैं, तो y = 10 - 2x का विचरण है:

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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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Detailed Solution

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दिया है

समान्तर माध्य = (μ) = 10

विचरण के गुणांक = CV = 40% या 0.4

सूत्र

CV = σ/μ

σ = मानक विचलन

μ = औसत 

गणना

0.4 = σ/10

⇒ σ/ = मानक विचलन = 0.4 × 10 = 4

अब, विचरण = V = (मानक विचलन)2 = σ2

विचरण = 42 = 16

हम जानते हैं कि 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

मानक विचलन का प्रतीक = σ

विचरण = मानक विचलन का वर्ग = σ2

विचरण गुणांक = CV = CV = σ/μ

μ = जनसंख्या माध्य

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