# 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:

### Steps to Solve

#### Apply the Geometric Mean Formula #### 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: 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.