Standaarddeviatie

Consider the goals scored by two teams with identical mean scores. To find out the better performing team, one can use standard deviation, another measure of variation, and compare the spread of all values from the mean.

The standard deviation formula depends on whether the data was drawn from a sample or from an entire population. If it's sample data, the standard deviation is denoted by s. For population data, it is represented by sigma. Note that the denominator is population size N for population data, instead of n minus 1 as in sample data.

If one plots the data from the example, the graph on the left shows more spread, hence, greater standard deviation. In contrast, the one on the right shows less spread and a smaller standard deviation. So, Team 2 is more consistent than Team 1.

Standard deviation values are usually positive and are zero only if all the dataset values are equal. The standard deviation and the dataset share the same units: here, it is the number of goals.