Standard Deviation:


The standard deviation (usually denoted by the Greek letter sigma: σ) is a statistic that indicates how tightly all data points are clustered around the mean in a set of data.

In a normal distribution, 68% of the data points fall within (positive and negative) 1 standard deviation of the mean. 95% of the points fall within (positive and negative) 2 standard deviations of the mean and 99.7% fall within (positive and negative) 3 standard deviations of the mean. Data sets with larger standard deviations have curves which are wider and flatter. Therefore, the standard deviation is a statistic that represents how data points are distributed around the mean. Larger standard deviations represent the existance of data points that, as a group, lie further away from the mean. 

There are a number of websites with applets that allow you to see the shape of a normal distribution defined by a given mean and standard deviation. Find one such site to verify that larger standard deviations result in wider and flatter curves.

It should be noted that this discussion of standard deviation was based on the normal curve or distribution. However, in any distribution, at least 89% of the data points lie within (positive and negative) 3 standard deviations of the mean.