Statistics
Standard Deviation
Grade 11
Question:
<p>The standard deviation of the data 6, 5, 9, 13, 12, 8, 10 is</p>
<p>\(\sqrt{\dfrac{52}{7}}\)</p>
<p>\(\dfrac{52}{7}\)</p>
<p>\(\sqrt{6}\)</p>
<p>6</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 this mean, and take the square root.
<p><strong>Step 1:</strong> Find the mean (average)<br/>Mean = (6 + 5 + 9 + 13 + 12 + 8 + 10) ÷ 7 = 63 ÷ 7 = 9</p><p><strong>Step 2:</strong> Calculate deviations from mean and square them<br/>(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 sum of squared deviations<br/>Sum = 9 + 16 + 0 + 16 + 9 + 1 + 1 = 52</p><p><strong>Step 4:</strong> Calculate variance<br/>Variance = 52 ÷ 7 = 7.43 (approximately)</p><p><strong>Step 5:</strong> Take square root to get standard deviation<br/>SD = √(52/7) = √7.43 ≈ 2.72 or √(52/7) = (2√91)/7</p><p>∴ Standard deviation ≈ 2.72 (or exact form: (2√91)/7)</p>
Correct Answer: A