How to Calculate the Geometric Mean

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Everyone knows about the arithmetic mean--the "average" of a set of numbers--and how to find it by adding the numbers up and dividing the sum (addition) by the number of numbers in the set. The lesser-known geometric mean is the average of the product (multiplication) of a set of numbers. Here is how to calculate it.

• Determine if you need the geometric mean. While the arithmetic mean calculates the average of a sum of numbers and cannot be used for ratios or percentages, the geometric mean can be used for quantities that have been multiplied by some factor and you need to find the "average" factor. The most common use of the geometric mean is to find the average rate of financial return.

• Know the formula for calculating the geometric mean. Simply stated, the geometric mean is the n-th root of the product of n numbers (data points). An example is shown in Steps 3 and 4.

• Multiply all of the data points and take the n-th root of the product. For example, to find the geometric mean of a set of two numbers (4 and 64), first multiply the two numbers to get a product of 256.

• Find the n-th root of the product. Since there are just two numbers in the data set, the n-th root is the square root of the product; if there were 10 numbers in the data set, you would find the 10th root For this example, the geometric mean is 16 (the square root of 256).

Tips & Warnings

• Use a scientific calculator to do the above calculation for data sets with more numbers. For example, for a data set of eight numbers, you would multiply the eight numbers together, press the equal key to get the product; then press the root key and the number eight to get the 8th root for the product.
• Calculate the average of the logs then convert to base 10 numbers if your calculator does not have the capability of finding an n-th root but does have a logarithmic (log or ln) key and anti-logarithms (exp or e) keys. Determine the logarithm of each data point using your calculator. Then add all the logarithms together and divide the sum by the number of data points in your set. This gives you the average of the log. You can then covert this log average back to a base 10 number by using the anti-logarithm key.
• Take advantage of spreadsheet functions to find geometric means. Microsoft Excel offers the "GeoMean" function from a series of data in a column.

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