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Different types of mean watch

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    I know of 3 types, the arithmetic mean, the geometric mean and harmonic mean.

    Arithmetic mean of 2 numbers a and b is given by
    \frac{a+b}{2}.

    Geometric mean of 2 numbers a and b is given by
    \sqrt{ab}.

    Harmonic mean of 2 numbers a and b is given by
    \frac{2ab}{a+b}.

    ...but why use different types of mean?
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    For an obvious one, if you want to measure the growth of something (e.g. share prices), using the geometric mean is most representative of the rate of overall growth.

    Harmonic mean makes sense for things like calculating average speeds. (e.g. if you drive a mile at x miles an hour and then a mile at y miles an hour, your average speed is the harmonic mean of x and y).
 
 
 
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Updated: March 11, 2008

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