Question:
If the variance of $1,2,3,\ldots,n$ is 10, then the value of $n$ is:
If the variance of $1,2,3,\ldots,n$ is 10, then the value of $n$ is:
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Memorize variance formula for $1$ to $n$ to save time in exams.
Updated On: Apr 30, 2026
- \(5 \)
- \(9 \)
- \(11 \)
- \(13 \)
- \(15 \)
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The Correct Option is C
Solution and Explanation
Concept:
Variance of first $n$ natural numbers:
\[
\sigma^2 = \frac{n^2 - 1}{12}
\]
Step 1: Substitute given variance.
\[ \frac{n^2 - 1}{12} = 10 \]
Step 2: Solve equation.
\[ n^2 - 1 = 120 \Rightarrow n^2 = 121 \Rightarrow n = 11 \]
Step 1: Substitute given variance.
\[ \frac{n^2 - 1}{12} = 10 \]
Step 2: Solve equation.
\[ n^2 - 1 = 120 \Rightarrow n^2 = 121 \Rightarrow n = 11 \]
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