What does the 'mean' mean in math?

Answer 1

"Mean" is another word for "average," and is calculated by dividing the sum of the numbers in the set by the number of terms in the set.

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True, as far as it goes. But it goes only as far as arithmetic mean. There are also the geometric and harmonic means.

The geometric mean of a set of n positive numbers is the nth root of their product.

The harmonic mean of two numbers x and y is 2/(1/x + 1/y)

Both definitions can be extended to three or more components.

Although the harmonic mean may appear to be a mathematical curiosity and a rather pointless measure, consider this example:

You travel a distance of 100 km at a speed of x km per hour. You drive back at y km per hour. What is your average speed for the round trip? It is NOT the "average" of x and y = (x+y)/2 but the harmonic mean of x and y.