Geometric Mean Calculator - Ungrouped & Grouped Data

Geometric Mean Calculator

Use this unified calculator to find the geometric mean for both ungrouped (raw) data and grouped (frequency distribution) data. The geometric mean is ideal for averaging rates of change and growth rates.

Quick Start

Understanding Geometric Mean

Geometric Mean is used for:

• Growth rates - annual percentage growth, compound growth
• Ratios - speed, rates of return, indices
• Positive values only - GM is undefined for zero or negative values
• Less affected by extremes than arithmetic mean (but more than median)

Formulas

Ungrouped Data: $$GM = \sqrt[n]{x_1 \times x_2 \times \cdots \times x_n} = \left(\prod_{i=1}^{n}x_i\right)^{1/n}$$

Ungrouped Data (Using Logarithms): $$\log(GM) = \frac{1}{n}\sum_{i=1}^{n}\log(x_i)$$

Grouped Data: $$GM = \sqrt[N]{x_1^{f_1} \times x_2^{f_2} \times \cdots \times x_n^{f_n}} = \left(\prod_{i=1}^{n}x_i^{f_i}\right)^{1/N}$$

Grouped Data (Using Logarithms): $$\log(GM) = \frac{1}{N}\sum_{i=1}^{n}f_i\log(x_i)$$

Where:

• N = total frequency (for grouped data)
• n = number of observations (for ungrouped data)
• fᵢ = frequency of class i

When to Use Geometric Mean

Related Calculators & Tutorials

Explore related measures:

• Arithmetic Mean
• Harmonic Mean
• Descriptive Statistics

Learn More:

• Measures of Central Tendency
• Mean Types and Applications