<p>Standard deviations for first 10 natural numbers is</p>
Step-by-Step Solution
Key Concept: Standard deviation measures spread around the mean. For the set {1,2,3,...,10}, use the formula SD = √(Σ(x-mean)²/n) or the computational formula SD = √(Σx²/n - (mean)²). The mean of first 10 natural numbers is 5.5.
<p><strong>Step 1:</strong> Find the mean of first 10 natural numbers: Mean = (1+2+3+...+10)/10 = 55/10 = 5.5</p><p><strong>Step 2:</strong> Calculate Σx² for 1 to 10: 1² + 2² + 3² + ... + 10² = 385</p><p><strong>Step 3:</strong> Use the computational formula: Variance = Σx²/n - (mean)² = 385/10 - (5.5)² = 38.5 - 30.25 = 8.25</p><p><strong>Step 4:</strong> Standard Deviation = √8.25 = √(33/4) = (√33)/2 ≈ 2.872</p><p>∴ Answer: D (SD = √8.25 or √(33/4) or approximately 2.87)</p>
Correct Answer: D