A standard deviation determines how spread out the values are in a set of data. The standard deviation is the measure of variability of any set of numerical values about their arithmetic mean and is represented by the Greek letter sigma. It is found by taking the square root of the variance, which is the average of the squared differences of the mean.
The standard deviation is a value used frequently in the social sciences and statistics, especially when discussing data printed in research papers or journals. The standard deviation can be useful in determining how to continue research or a course of action depending on how much variance exist in the data. For example, a teacher who finds there is a large value for the standard deviation of test scores, indicating there is great variance, may choose to adjust his teaching method to accommodate students of various backgrounds and aptitudes. When test scores indicate there is little variance, represented by a small standard deviation, and when they're consistently high, there may be little concern over how to instruct the class or make up the lesson plans. There are two types of standard deviations: population standard deviation and sample deviation.