Geometric Mean Calculator

What is the Geometric Mean?

The geometric mean is a type of average that is useful for sets of numbers with different ranges. It's calculated by multiplying all numbers in a set and then taking the nth root of the product, where n is the count of numbers.

Formula and Its Meaning

The formula for the geometric mean (GM) is:

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

Where:

• \(x_1, x_2, \ldots, x_n\) are the individual values in a dataset
• \(n\) is the number of values

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 Calculation

Let's calculate the geometric mean for the dataset: 2, 8, 32

1. Multiply the numbers: \(2 \times 8 \times 32 = 512\)
2. Take the cube root (since there are 3 numbers): \(\sqrt[3]{512} \approx 8\)

Visual Representation

This logarithmic scale plot represents the example dataset. The red dashed line indicates the geometric mean (8).