Geometric Mean Calculator
Find the geometric mean of a data set by entering the numbers in the set below.
|Geometric Mean x̄g:|
|Numbers in Set:|
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
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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:
xi = each number in the set
n = number of elements in the set
So, the geometric mean x̄g 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.
x̄g = 4√210
x̄g = 3.806754
So, the geometric mean x̄g of the data set above is roughly equal to 3.806754.