# Definition Arithmetic mean

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 chocolate bars. John eats six bars, Harry five, Paul one, and Conrad none. Together, the friends ate 12 chocolate bars. On average, each ate three bars ([6+5+1+0]:4=3). The example illustrates the problem of the mean – it can fudge results, especially if the single observations strongly differ from each other. On average, each person ate three bars, when, in fact, one of the friends did not eat any bar and another only one. Oftentimes, 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.

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