Geometric Mean Calculator

Find the geometric mean of a data set by entering the numbers in the set below.

Separate numbers using a comma (,)

Results:

Geometric Mean g:
 
Numbers in Set:
 

Steps to Solve

Apply the Geometric Mean Formula

graphic showing the geometric mean formula where the geometric mean is equal to the nth root of the product of all numbers in the set, where n is the count of numbers in the set

Step One: Find the Product of the Numbers in the Set

Product = x1 · x2 ··· xn

Step Two: Find the Nth Root

Geometric Mean x̄g = nProduct



How to Find the Geometric Mean

In statistics, the geometric mean is the average of a data set that is found using the nth root of the product of each number in the set, where n is the size of the set.

The geometric mean is similar to the arithmetic mean in that it is a measure of the central tendency of the data, but instead of measuring the center using addition and division, it uses multiplication and the root.

The geometric mean is a way of measuring the average of a progression of data, which is why it’s often used in finance, investing, and economics.

Geometric Mean Formula

As we mentioned above, the geometric mean is the nth root of the product of the numbers in the set, so the geometric mean formula is:

graphic showing the geometric mean formula where the geometric mean is equal to the nth root of the product of all numbers in the set, where n is the count of numbers in the set

Where:
xi = each number in the set
n = number of elements in the set

So, the geometric mean g is equal to the nth root product of each number xi in the set, where n is equal to the number of elements in the set.

Using the formula, you can find the geometric mean in a few steps.

Find the Product

First, find the product of all of the numbers in the set. You can do this by multiplying each number in the set together.

Find the Root

Then, count the number of items in the set. Once you have the count, take the nth root of the product.

For example: let’s find the geometric mean for the numbers [2,3,5,7]

Let’s start by finding the product of all of the numbers.

product = 2 · 3 · 5 · 7
product = 210

Then, let’s take the nth root of 210, with n being equal to 4, since there are four numbers in the set.

g = 4√210
g = 3.806754

So, the geometric mean g of the data set above is roughly equal to 3.806754.