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# arithmetic mean

The arithmetic mean, also called the average or average value, is the quantity obtained by summing two or more numbers or variables and then dividing by the number of numbers or variables. The arithmetic mean is important in statistics.

When there are only two quantities involved, the arithmetic mean is obtained simply by adding the quantities and dividing by 2. In these cases, the operation is sometimes symbolized by a double colon (::) between the two quantities to be averaged. For example:

3 :: 11 = 7-10 :: +4 = -3

The determination of the average of a large number of quantities is a tedious task; computers are commonly used to calculate these values.

The arithmetic mean of a continuous function over a defined interval is determined by first calculating the definite integral over the interval, and then dividing this quantity by the width of the interval.

Also see Mathematical Symbols.

This was last updated in September 2005
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