A geometric mean gives you the true average of any given data. Geometric averages are one out of three parts of what is known as a Pythagorean mean analysis of data.
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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".