Statistics
Coefficient of Variation
Grade 11
Question:
<p>For a given distribution of marks, the mean is 35.16 and its standard deviation is 19.76. The coefficient of variation is</p>
<p>\(\dfrac{35.16}{19.76}\)</p>
<p>\(\dfrac{19.76}{35.16}\)</p>
<p>\(\dfrac{35.16}{19.76} \times 100\)</p>
<p>\(\dfrac{19.76}{35.16} \times 100\)</p>
Step-by-Step Solution
Key Concept: Coefficient of variation (CV) is the ratio of standard deviation to mean, expressed as a percentage. It measures relative variability independent of units and scale.
<p><strong>Step 1:</strong> Recall the formula for Coefficient of Variation (CV):</p><p>CV = (Standard Deviation / Mean) × 100%</p><p><strong>Step 2:</strong> Substitute the given values:</p><p>Mean = 35.16</p><p>Standard Deviation = 19.76</p><p><strong>Step 3:</strong> Calculate CV:</p><p>CV = (19.76 / 35.16) × 100</p><p>CV = 0.5621 × 100</p><p>CV = 56.21%</p><p><strong>Step 4:</strong> Rounding appropriately:</p><p>CV ≈ 56.2% or 56.21%</p><p>∴ Answer: D</p>
Correct Answer: D