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13.Statistics
medium
संख्याओं $1, 2, 3, 4, 5, 6$ का माध्य तथा मानक विचलन है
A
$\frac{7}{2},\,\sqrt {\frac{{35}}{{12}}} $
B
$3, 3$
C
$\frac{7}{2},\,\sqrt 3 $
D
$3,\,\frac{{35}}{{12}}$
Solution
(a)माध्य $\bar x = \frac{{1 + 2 + 3 + 4 + 5 + 6}}{6}$
$ = \frac{{21}}{6} = \frac{7}{2}$
मानक विचलन ($S.D.$) $ = \sigma = \sqrt {\frac{1}{n}\Sigma x_i^2 – {{(\bar x)}^2}} $
$ = \sqrt {\frac{1}{6}(1 + 4 + 9 + 16 + 25 + 36) – \frac{{49}}{4}} $
$ = \sqrt {\frac{{91}}{6} – \frac{{49}}{4}} $
$ = \sqrt {\frac{{182 – 147}}{{12}}} $
$ = \sqrt {\frac{{35}}{{12}}} $.
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Standard 11
Mathematics
