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13.Statistics
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પ્રથમ $50 $ યુગ્મ પ્રાકૃતિક સંખ્યાઓનું વિચરણ .. . . . . .છે.
A
$437$
B
$\frac{{437}}{4}$
C
$\frac{{833}}{4}$
D
$833$
(JEE MAIN-2014)
Solution
$2,4,6,8,……,98,100$
${\sigma ^2} = \frac{{\sum x_1^2}}{n} – {\left( {\overline {.x} } \right)^2}$
$\frac{{{2^2} + {4^2} + {6^2} + …. + {{100}^2}}}{{50}}$$ – {\left( {\frac{{2 + 4 + 6 + …. + 100}}{{50}}} \right)^2}$
${i_1} = \frac{{{2^2} + {4^2} + {6^2} + …. + {{100}^2}}}{{50}}$
$ = {2^2}\frac{{{1^2} + {2^2} + {3^2} + … + {{50}^2}}}{{50}}$
$ = \frac{{{2^2}}}{{50}} \times 50\left( {50 + 1} \right)\left( {100 + 1} \right)$
$ = 3434$
${i_2} = {\left( {\frac{{2 + 4 + 6 + ….. + 100}}{{50}}} \right)^2}$
$ = {\left( {\frac{{50 \times \frac{{2 + 100}}{2}}}{{50}}} \right)^2}$
$ = {\left( {51} \right)^2}$
${\sigma ^2} = 3434 – 2661 = 833$
Standard 11
Mathematics