$\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.

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