Question:
Variance of first 20 natural numbers
Variance of first 20 natural numbers
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Use standard formulas for sums of natural numbers.
Updated On: May 1, 2026
- \( \frac{399}{2} \)
- \( \frac{379}{12} \)
- \( \frac{133}{2} \)
- \( \frac{133}{4} \)
- \( \frac{169}{2} \)
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The Correct Option is D
Solution and Explanation
Concept: Variance formula:
\[
\sigma^2 = \frac{\sum x^2}{n} - \mu^2
\]
Step 1: Mean: \[ \mu = \frac{21}{2} \]
Step 2: Sum squares: \[ \frac{20\cdot21\cdot41}{6} \]
Step 3: Compute mean of squares.
Step 4: Substitute in formula.
Step 5: Final: \[ \frac{133}{4} \]
Step 1: Mean: \[ \mu = \frac{21}{2} \]
Step 2: Sum squares: \[ \frac{20\cdot21\cdot41}{6} \]
Step 3: Compute mean of squares.
Step 4: Substitute in formula.
Step 5: Final: \[ \frac{133}{4} \]
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