<p>If the sum of the deviations of 50 observations from 30 is 50, then the mean of these observations is:</p>
Step-by-Step Solution
Key Concept: The sum of deviations from any value equals n(mean - that value). Use this formula to find the actual mean by setting up the equation: Σ(xᵢ - 30) = 50.
<p><strong>Step 1:</strong> Recall the fundamental property: if deviations are taken from some value 'a', then Σ(xᵢ - a) = n(x̄ - a), where x̄ is the mean and n is the number of observations.</p><p><strong>Step 2:</strong> Apply the formula with a = 30, n = 50, and Σ(xᵢ - 30) = 50:</p><p>50 = 50(x̄ - 30)</p><p><strong>Step 3:</strong> Solve for the mean:</p><p>50 = 50x̄ - 1500</p><p>1550 = 50x̄</p><p>x̄ = 31</p><p>∴ Answer: D (Mean = 31)</p>
Correct Answer: D