CBSE BoardEnglish MediumSTD 11 ScienceMathsStatistics1 Mark
Question
Write the variance of first n natural numbers.
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Answer
Variance $=\sum\frac{\text{x}^2}{\text{n}}-\Big(\sum\frac{\text{x}}{\text{n}}\Big)^2$
But $\sum\text{x}=1+2+3+....+\text{n}=\text{n}\Big(\text{n}+\frac{1}{2}\Big)$
$\sum\text{x}^2=\frac{\text{n}(\text{n}+1)(2\text{n}+1)}{6}$
Substituting these value we get
Variance = $=\frac{(\text{n}^2-1)}{12}$
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