# Find the standard deviation of the data: $6,5,9,13,12,8,10$ is

$\begin{array}{1 1}(A)\; \sqrt {2}\\(B)\;2.57\\(C)\;3\\(D)\;\sqrt {\large\frac{52}{7}}\end{array}$

Toolbox:
• The formula to calculated SD is
• $SD= \sqrt {\large\frac{\sum x^2}{n} - \bigg( \large\frac{\sum x}{n}\bigg)^2}$
$n=7$
$x_i= 6 ;\qquad x_i^2 =36$
$x_i= 5 ;\qquad x_i^2 =25$
$x_i= 9 ;\qquad x_i^2 =81$
$x_i= 13 ;\qquad x_i^2 =169$
$x_i=12 ;\qquad x_i^2 =144$
$x_i= 8 ;\qquad x_i^2 =64$
$x_i= 10 ;\qquad x_i^2 =100$
Total $\sum x_i =63 \;\qquad \sum x_i^2 =619$
$SD = \sqrt {\large\frac{\sum x^2}{n} -\bigg( \large\frac{\sum x}{n}\bigg)^2}$
$\qquad= \sqrt { \large\frac{619}{7} - \bigg(\large\frac{63}{7}\bigg)^2}$
$\qquad= \large\frac{1}{7} $$\sqrt {619 \times 7 -63^2} \qquad= \large\frac{1}{7}$$ \sqrt {4333-3969}$
$\qquad= \large\frac{1}{7} $$\sqrt { 364} \qquad= \large\frac{1}{7}$$\sqrt {364}$
$\qquad= \large\frac{1}{7}$$\sqrt {364}$
$\qquad= \sqrt { \large\frac{364}{7 \times 7}}$
$\qquad=\sqrt{ \large\frac{52}{7}}$
Hence D is the correct answer.
answered Jul 8, 2014 by