Descriptive Statistics

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 the applet below, chose a mean and enter several standard deviation values. What happens to the shape of the curve as the standard deviation values increase? .

Graph of the Normal Distribution

The curve in the applet is a normal curve. 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. Note that as you increased the standard deviation in the applet, the curve became wider and flatter. Therefore, the standard deviation is a statistic that represents how data points are distributed around the mean. Larger standard deviations represent data points that lie further away from the mean.

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.