Definition Arithmetic mean

The arithmetic mean describes the statistical average and ranks among the location parameters in summary statistics.

The arithmetic mean is the sum of all values in a data set divided by the number of values in that data set.

An example:

Four friends spend the evening drinking beer. John drinks six bottles, Harry five, Paul one and Conrad drinks zero beers. Together, the friends drank 12 beers, on average each drank 3 beers ([6+5+1+0]:4=3).

The example illustrates the problem of the mean – it can fudge results, especially if there is an extreme deviation. On average, each man drank three beers, when in fact there are two sober men at the table sitting across from two relatively drunk men. Often times the mean provides a good orientation (e.g. average fuel consumption of a car, average salaries, etc.), but it must be examined critically. 

Please note that the definitions in our statistics encyclopedia are simplified explanations of terms. Our goal is to make the definitions accessible for a broad audience; thus it is possible that some definitions do not adhere entirely to scientific standards.