Pooled standard deviation

Method for estimating a single standard deviation to represent all independent samples or groups in your study when they are assumed to have a common standard deviation. The pooled standard deviation is the average spread of all data points about their group mean (not the overall mean). It is a weighted average of each group's standard deviation. The weighting gives larger groups a proportionally greater influence on the overall estimate. Pooled standard deviations are used in t-tests, ANOVAs, control charts, and capability analysis.

For example, your study has the following four groups:

Pooled standard deviation = 5.486

The first three groups are equal in size (n=50) with standard deviations around 3. The fourth group is much larger (n=200) and has a higher standard deviation (6.8). Because the pooled standard deviation uses a weighted average, its value (5.486) is closer to the standard deviation of the largest group. If a simple average had been used, then all groups would have had equal influence.