Flatness: what it means and how to read it
In the report: 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.
How to read it
From 0 to 1 for positive values: 1 — all values are equal; close to 0 — a few large values stand far above the rest.
In plain words
A teacher gave four groups the same task and wanted to know whether the points were shared evenly. In the first round every group got 10 points, and flatness came out 1, which means all the numbers are equal. In the second round the groups got 1, 1, 1 and 37 points. The average is still 10, but flatness came out about 0.25. Close to zero means one or two big numbers stand far above the rest. Now she can tell that in the second round almost all of the points went to one group. A group with 0 points would make flatness exactly zero.
How it is computed
geometricMean / meanWhere you see it
STATS_DESCRIPTIVE— Column-wise descriptive statistics with flexible metric selection and optional column filtering.
Related values
- 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.
- Sum of squared deviations — The sum of the squared deviations from the mean: Σ (x − x̄)²; empty for a column without a single number, 0 for one value.
- Inverse-variance weight — n / variance; empty for a column without spread or with fewer than 2 values.
Get it in your sheet
One formula in a cell gives the whole report, Flatness included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)