# Geometric Mean Calculator

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

## Results:

Geometric Mean x̄_{g}: | |
---|---|

Numbers in Set: |

### Steps to Solve

#### Apply the Geometric Mean Formula

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

Product = x_{1} · x_{2} ··· x_{n}

#### Step Two: Find the Nth Root

Geometric Mean x̄_{g} = ^{n}Product

## 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:

Where:

x_{i} = each number in the set

n = number of elements in the set

So, the geometric mean *x̄ _{g}* is equal to the

*nth*root product of each number

*x*in the set, where

_{i}*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.

x̄_{g} = ^{4}√210

x̄_{g} = 3.806754

So, the geometric mean *x̄ _{g}* of the data set above is roughly equal to 3.806754.