# Professor Puzzler's Statistics Calculator

Provide a data set below, and find out all you need to know!Geometric mean Detailed analysisAverageMedianModeRangeOutliersStandard deviationHarmonic meanQuartilesIQRVariance# Geometric Mean

*Please enter data above to calculate the geometric mean.*

## Explanation

The geometric mean is obtained by taking the product of the data points, and then taking the n^{th}root of the product, where n is the number of points in the set.

Geometric means are always less than or equal to the arithmetic mean of the same number.

Under what circumstances will a geometric mean not exist? There are two ways of answering this question. The first way is that if you have an even number of data points, and an odd number of those points is negative, this will result in an even root of a negative number, which is not defined. The second way is to say that a geometric mean is of no practical value unless all the points are positive. If even one point is zero, the mean is zero, which provides little useful information, and if one or more points is negative, even if the mean is possible to calculate, the result would have little relavence to the actual data, since the same result would be obtained if different numbers in the set were negative.

For more information about geometric means, visit our reference unit on Pythagorean Means.

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