How many kinds of average are there?

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I have learned that the mean, median and mode are three kinds of average.

Are there other kinds of average or are there just these three ?

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There are two main categories of averages. One, mathematical averages focus on using mathematical tools to find the "average". These are Arithmetic, Geometric, and Harmonic Means. The Positionals are concerned with finding values within the data set only, these are Median and Mode. However, if you wish to, you can arbitrarily create new "averages" for usage in different situations with finding values within the data set only.