<p>The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is</p>
Step-by-Step Solution
Key Concept: Standard deviation measures spread from the mean. Calculate mean first, then find the average of squared deviations from that mean, and take the square root.
<p><strong>Step 1:</strong> Find the mean of the data: 6, 5, 9, 13, 12, 8, 10</p><p>Mean = (6 + 5 + 9 + 13 + 12 + 8 + 10)/7 = 63/7 = 9</p><p><strong>Step 2:</strong> Calculate squared deviations from mean:</p><p>(6-9)² = 9, (5-9)² = 16, (9-9)² = 0, (13-9)² = 16, (12-9)² = 9, (8-9)² = 1, (10-9)² = 1</p><p><strong>Step 3:</strong> Find variance (average of squared deviations):</p><p>Variance = (9 + 16 + 0 + 16 + 9 + 1 + 1)/7 = 52/7</p><p><strong>Step 4:</strong> Standard deviation = √(52/7) = √(52/7) = 2√(13/7) = (2√91)/7 ≈ 2.73</p><p>∴ Answer: A</p>
Correct Answer: A