Geometric mean
Average growth rate

In many cases the geometric mean is the best measure to determine the average growth rate of some quantity. For instance, if sales increases by 80% in one year and the next year by 25%, the end result is the same as that of a constant growth rate of 50%, since the geometric mean of 1.80 and 1.25 is 1.50. In order to determine the average growth rate, it is not necessary to take the product of the measured growth rates at every step. Let the quantity be given as the sequence a 0, a 1,..., a n {\displaystyle a_{0},a_{1},...,a_{n}}, where n {\displaystyle n} is the number of steps from the initial to final state. The growth rate between successive measurements a k {\displaystyle a_{k}} and a k + 1 {\displaystyle a_{k+1}} is a k + 1 / a k {\displaystyle a_{k+1}/a_{k}}. The geometric mean of these growth rates is then just:
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