Enter a set of numbers to compute the geometric mean.
Calculate the Geometric Mean of a Set of Numbers
Result
What Is the Geometric Mean?
The geometric mean is a measure of central tendency used to calculate the average of a set of positive numbers. Unlike the arithmetic mean, it is calculated by taking the \( n \)-th root of the product of all numbers in the dataset. It is especially useful for data involving ratios, percentages, or exponential growth. The formula is:
\( G = \sqrt[n]{\prod_{i=1}^{n} x_i} \)
Where:
\( n \) is the total number of data points,
\( x_i \) represents each individual data point,
\(\prod\) denotes the product of the numbers.
How to Calculate the Geometric Mean?
Steps:
Multiply all the numbers together to get their product.
Take the \( n \)-th root of the product, where \( n \) is the total number of data points.
Data Entry Notes:
All numbers must be positive.
Custom delimiters (e.g., commas, semicolons, line breaks) are supported.
Thousands separators (e.g., 100,000) are supported.
Examples
Example 1: Calculate the Geometric Mean of 4, 8, and 16
Solution:
1. Calculate the product:
\( 4 \times 8 \times 16 = 512 \)
2. Geometric Mean:
\( G = \sqrt[3]{512} = 8 \)
Example 2: Calculate the Geometric Mean of 2, 18, and 50