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13.Statistics
medium
प्रथम $n$ प्राकृत संख्याओं का प्रसरण है
A
$\frac{{{n^2} - 1}}{{12}}$
B
$\frac{{{n^2} - 1}}{6}$
C
$\frac{{{n^2} + 1}}{6}$
D
$\frac{{{n^2} + 1}}{{12}}$
Solution
(a) प्रसरण $ = {({\rm{S}}{\rm{.D}}{\rm{.}})^2}$$ = \frac{1}{n}\Sigma {x^2} – {\left( {\frac{{\Sigma x}}{n}} \right)^2}$, $\left( {\because \;\;\bar x = \frac{{\Sigma x}}{n}} \right)$
$ = \frac{{n(n + 1)\;(2n + 1)}}{{6n}} – {\left( {\frac{{n(n + 1)}}{{2n}}} \right)^2} $
$= \frac{{{n^2} – 1}}{{12}}$.
Standard 11
Mathematics
