Statistics
Variance
Grade 11
Question:
<p>If the mean of the data: 7, 8, 9, 7, 8, 7, \(\lambda\), 8 is 8, then the variance of this data is</p>
<p>\(\dfrac{7}{8}\)</p>
<p>1</p>
<p>\(\dfrac{9}{8}\)</p>
<p>2</p>
Step-by-Step Solution
Key Concept: First find λ using the mean condition, then calculate variance using the formula σ² = (Σx²/n) - (mean)². The variance depends critically on finding the correct value of λ from the mean equation.
<p><strong>Step 1: Find λ using the mean condition</strong></p><p>Mean = (7 + 8 + 9 + 7 + 8 + 7 + λ + 8)/8 = 8</p><p>(54 + λ)/8 = 8</p><p>54 + λ = 64</p><p>λ = 10</p><p><strong>Step 2: Calculate Σx² with the complete data: 7, 8, 9, 7, 8, 7, 10, 8</strong></p><p>Σx² = 49 + 64 + 81 + 49 + 64 + 49 + 100 + 64 = 520</p><p><strong>Step 3: Apply variance formula</strong></p><p>Variance = (Σx²/n) - (mean)²</p><p>Variance = (520/8) - (8)²</p><p>Variance = 65 - 64</p><p>Variance = 1</p><p>∴ Answer: C</p>
Correct Answer: C