Question

Find the standard deviation for the following data:

$x_i$	3	8	13	18	23
$f_i$	7	10	15	10	6

• A. $6.12$
• B. $5.12$
• C. $3.12$
• D. $7.12$

Answer 1

Answer: (A)

Let us form the following table:

$x_i$	$f_i$	$f_i{x}_i$	$x_i^2$	$f_i{x}_i^2$
3	7	21	9	63
8	10	80	64	640
13	15	195	169	2535
18	10	180	324	3240
23	6	138	529	3174
Total	48	614		9652

Now, $\left(\sigma \right)=\frac{1}{N}\sqrt{N\Sigma f_i{x}_i^2-{\left(\Sigma f_i{x}_i\right)}^2}$
$=\frac{1}{48}\sqrt{48\times 9652-{\left(614\right)}^2}$
$=\frac{1}{48}\sqrt{463296-376996}$
$=\frac{1}{48}\times 293.77$
$=6.12$