I'm posting a link which explains it pretty good, but here it is. Given a set of n numbers, the Geometric mean is found by multiplying all of the numbers together, then taking the nth root of this product. The nth root can also be written as taking to the 1/n power.
Example: Geometric mean of 8 and 2: There are two numbers, so take the square root of the product. sqrt(8*2) = sqrt(16) = 4.
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No, the geometric mean is not the same as the mean of two numbers.
The geometric mean is 35.0
The geometric mean of 9 and 81 is 27.0
The geometric mean of 9 and 25 is: 15.0
You can find the differences between arithmetic and geometric mean in the following link: "Calculation of the geometric mean of two numbers".