# Standard Deviation

The Standard deviation of a data set shows how much variance the data has from the mean. A low standard deviation entails that the data points are clustered close to the mean, and the data has a small range.  If you have a high standard deviation then the data points are spread widely over a large range. Standard deviation is a good way to measure confidence in results

A sample’s standard deviation is usually represented by the variable ‘s’; while the entire population’s standard deviation is denoted by the variable ‘$\sigma$‘.

Standard Deviation Equation:

$s=\sqrt{\frac{(\sum(y-\overline{y})^2)}{n-1}}$

You can find a basic definition of standard deviation, and a bit of background on where the equation comes from at this site. Here you can find help with finding standard deviations in SPSS. For help on how and why to use the standard deviation when analyzing data, you should read this.