Report a Geometric Mean on the Correct Scale

Establish why a log-scale summary is useful

A geometric mean summarizes positive values through their logarithms. It can be useful when ratios and multiplicative variation match the scientific question, but it is not an automatic remedy for every skewed distribution. Start by recording the measurement, units, eligible population, and reason for using the log scale.

The official SciPy geometric-mean documentation defines the calculation as exponentiating the mean of logarithms for equally weighted observations. This is a different summary from the arithmetic mean, not an alternative way of computing the same quantity.

Check the input domain

The demonstration tool requires strictly positive numerical values. Investigate zeros, negative values, and codes for missingness or results below a detection limit. Do not add one or another arbitrary constant solely to make logarithms possible: that changes the resulting summary and its interpretation.

Retain the raw measurements and document any scientifically justified transformation or censoring method separately. A value reported below an assay threshold is not necessarily zero, and an omitted result should not quietly become a small positive number.

Work through fictional values

Consider the fictional measurements 1, 4, and 16 in the same units. Their product is 64, so the cube root is 4. Equivalently, their natural logs are 0, approximately 1.386294, and approximately 2.772589; the mean log is approximately 1.386294 and its exponential is 4.

The arithmetic mean is 7, which answers a different descriptive question. The geometric-summary tool illustrates the log-scale calculation. The sample SD of the natural logs is approximately 1.386294, so the tool's geometric SD, its exponential, is 4. This is a multiplicative spread factor, not an additive SD or confidence interval.

Distinguish location, spread, and uncertainty

A geometric mean should not be displayed with an arithmetic SD as though their combination were a conventional symmetric summary. The tool accepts 2–200 strictly positive synthetic values and does not calculate a confidence interval. If reporting geometric spread, explain its definition and multiplicative meaning. If reporting an interval for the mean log transformed back to the original scale, identify the interval method and assumptions separately.

Use the log-scale summary worksheet to document the transformation base, input handling, summary definition, and reporting units. The exponential of a mean log is not generally the arithmetic population mean. Predicting an arithmetic mean from a log-scale model can require additional assumptions and correction.

Inspect the distribution of the logged observations and any influential values before selecting an inferential method. Positive data alone do not guarantee normality after logging, independent observations, or reliable small-sample inference.

Finish with a plainly labeled geometric mean, observed sample size, units, and an explanation of any accompanying spread or interval. Preserve enough detail for a reader to reproduce the transformation without guessing how zeros, missing results, or detection limits were handled.

Source checked on 3 November 2026; fictional logarithms independently recalculated.