Geometric Mean Calculator

How to Calculate Geometric Mean

The Geometric Mean is a type of average that is useful for sets of numbers with different ranges. It's often used to calculate average growth rates in finance and population studies.

Formula

The Geometric Mean (GM) of n numbers is calculated using the formula:

\[ GM = \sqrt[n]{x_1 \times x_2 \times ... \times x_n} \]

Where:

• \(x_1, x_2, ..., x_n\) are the numbers in the dataset
• \(n\) is the count of numbers

Calculation Steps

1. Multiply all numbers in the dataset
2. Take the nth root of the product, where n is the count of numbers

Example

Let's calculate the Geometric Mean of the numbers 2, 4, and 8:

1. Multiply the numbers: 2 × 4 × 8 = 64
2. Take the cube root (since there are 3 numbers): \(\sqrt[3]{64} = 4\)

Therefore, the Geometric Mean is 4.

Visual Representation

This diagram illustrates the Geometric Mean of 2, 4, and 8. The bars represent the input numbers, and the dashed red line shows the Geometric Mean at 4.