<p>The following information relates to a sample of size 60: \(\Sigma x^2 = 18000\), \(\Sigma x = 960\). The variance is</p>
Step-by-Step Solution
Key Concept: Variance formula: σ² = (Σx²/n) - (Σx/n)². You must calculate the mean first, then use the computational formula to avoid arithmetic errors.
<p><strong>Step 1:</strong> Identify given data: n = 60, Σx² = 18000, Σx = 960</p><p><strong>Step 2:</strong> Calculate the mean: x̄ = Σx/n = 960/60 = 16</p><p><strong>Step 3:</strong> Apply variance formula: σ² = (Σx²/n) - (x̄)²</p><p><strong>Step 4:</strong> Substitute values: σ² = (18000/60) - (16)²</p><p><strong>Step 5:</strong> Calculate: σ² = 300 - 256 = 44</p><p>∴ Answer: D (Variance = 44)</p>
Correct Answer: D