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Standard deviations for first 10 natural number is

$\begin{array}{1 1}(A)\; 5.5 \\(B)\;3.87 \\(C)\;2.97 \\(D)\;2.87 \end{array} $

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  • The formula to calculate SD is $SD= \sqrt {\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2}$
1st 10 natural numbers are 1,2,3,4,5,6,7,8,9,10
$\sum x = 1+2+3+4+5+6+7+8+9+10$
$\qquad = \large\frac{n(n+1)}{2} =\large\frac{10(10+1)}{2}$
$\qquad=\large\frac{10 \times 11}{2} $$=55$
$\sum x^2 =1^2+2^2+..............+10^2$
$\qquad= \large\frac{n(n+1)(2n+1)}{6}$
$\qquad= \large\frac{10 \times 11 \times 21}{6}$
$\qquad= 385$
$SD= \sqrt {\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2}$
$\qquad= \sqrt {\large\frac{385}{10} - \bigg( \large\frac{55}{10}\bigg)^2}$
$\qquad= \sqrt {38.5 -(5.5)^2}$
$\qquad= \sqrt {8.25 }$
$\qquad= 2.87$
Hence D is the correct answer.
answered Jul 8, 2014 by meena.p

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