# Standard Deviation

Standard deviation is the measure of how spread out your data is.  It is a statistic that tells you how closely all of the examples are gathered around the mean (average) in a data set.  The steeper the bell curve, the smaller the standard deviation.  If the examples are spread far apart, the bell curve will be much flatter, meaning the standard deviation is large.  In business, the smaller the standard deviation is the better.

### Procedure for Finding the Standard Deviation:

$1$ .  Find the mean of the scores $\left(\stackrel{¯}{x}\right)$ .

$2$ .  Subtract the mean from each individual score $\left(x-\stackrel{¯}{x}\right)$ .

$3$ .  Square each of the differences obtained above.  ${\left(x-\stackrel{¯}{x}\right)}^{2}$ .

$4$ .  Add all of the squares obtained in step $3$ . $\left(\sum {\left(x-\stackrel{¯}{x}\right)}^{2}\right)$ .

$5$ .  Divide the total from step $4$ by the number ( $n-1$ ), where $n$ is the total number of scores used.

$6$ .  Find the square root of the result of step $5$ .

Be careful not to round the mean too much as the resulting standard deviation can be in error.  Try not to round any intermediate results.  Round only at the end.