Mean and S.D. of 1, 2, 3, 4, 5, 6 is

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13.Statistics

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The mean and $S.D.$ of $1, 2, 3, 4, 5, 6$ is

A

$\frac{7}{2},\,\sqrt {\frac{{35}}{{12}}} $

B

$3, 3$

C

$\frac{7}{2},\,\sqrt 3 $

D

$3,\,\frac{{35}}{{12}}$

Solution

(a) Mean $\bar x = \frac{{1 + 2 + 3 + 4 + 5 + 6}}{6}$

$ = \frac{{21}}{6} = \frac{7}{2}$

$S.D.$ $ = \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}}} $.

Standard 11

Mathematics

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