<p>Coefficients of variation of two distributions are 50 and 60, and their arithmetic means are 30 and 25, respectively. Difference of their standard deviations is</p>
Step-by-Step Solution
Key Concept: Coefficient of Variation (CV) = (Standard Deviation / Mean) × 100. Use this formula to find individual standard deviations, then compute their difference.
<p><strong>Step 1:</strong> Recall the formula for Coefficient of Variation: CV = (σ/μ) × 100, where σ is standard deviation and μ is arithmetic mean.</p><p><strong>Step 2:</strong> For Distribution 1: CV₁ = 50, Mean₁ = 30<br/>50 = (σ₁/30) × 100<br/>σ₁ = (50 × 30)/100 = 15</p><p><strong>Step 3:</strong> For Distribution 2: CV₂ = 60, Mean₂ = 25<br/>60 = (σ₂/25) × 100<br/>σ₂ = (60 × 25)/100 = 15</p><p><strong>Step 4:</strong> Difference of standard deviations = |σ₂ - σ₁| = |15 - 15| = 0</p><p>∴ Answer: A (The difference is 0)</p>
Correct Answer: A