Geometric mean: what it means and how to read it
In the report: geometricMean — The n-th root of the product of the values; zero and tiny values are raised to epsilon (Settings), a negative value gives an empty cell.
How to read it
The right average for growth rates and ratios: growth of ×1.1 and ×0.9 averages to ×0.995 per year, not ×1. For ordinary scores use the mean.
In plain words
An investor made 10 percent in the first year and lost 10 percent in the second. The plain average of plus 10 and minus 10 is zero, as if nothing changed. But 100 dollars grew to 110 and then fell to 99. She wanted the honest average change per year. She wrote each year as what 100 dollars became: 110 and 90. geometricMean of these two came out 99.5. Now she can say that each year every 100 dollars ended up at about 99 and a half, a loss of about half a dollar a year on every 100. For ordinary marks, use the plain average; this one is for growth.
How it is computed
exp(Σ ln x / n)Where you see it
STATS_DESCRIPTIVE— Column-wise descriptive statistics with flexible metric selection and optional column filtering.
Related values
- Harmonic mean — n divided by the sum of 1/x; zero and tiny values are raised to epsilon (Settings), a negative value gives an empty cell.
- Flatness — The geometric mean of the values as they are divided by their arithmetic mean, without epsilon: a zero among the values gives exactly 0; empty when the mean is 0 or a value is negative.
- Spectral flatness — The geometric mean divided by the arithmetic mean of the shares x² / Σ x².
- Slope from the first to the last value — (last value − first value) / (n − 1), in row order; empty for fewer than 2 values, 0 for a constant.
- Sum of squared values — The sum of the squared values: Σ x²; empty for a column without a single number.
Get it in your sheet
One formula in a cell gives the whole report, Geometric mean included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)