The answer is very simple: only terminology is different. The number that statisticians call mean is the same with the number that mathematicians call average. This is because, even though mean refers to the same thing as average by default, there are other forms of it, such as the geometric or harmonic mean. What we call mean and can call average , is also known as the arithmetic mean. The geometric mean is the number that you get when you multiply all the values in the list and then find the square root if you have 2 numbers , cube root if you have 3 numbers , etc, of this number.
To find the harmonic mean , you need to find the arithmetic mean at first. The reciprocal of this number of the sum of reciprocals of the given set of values will give you the harmonic mean.
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