Harmonic mean: what it means and how to read it
In the report: harmonicMean — n divided by the sum of 1/x; zero and tiny values are raised to epsilon (Settings), a negative value gives an empty cell.
How to read it
The right average for rates: 60 and 30 km/h over equal distances average to 40 km/h, not 45.
In plain words
A driver went to a town 60 kilometres away at 60 kilometres an hour and came back at 30 kilometres an hour. He wanted to know his average speed. It is tempting to say 45. But the way there took 1 hour and the way back took 2 hours, so he covered 120 kilometres in 3 hours: 40 an hour. He asked for harmonicMean of the two speeds and it gave exactly 40. Now he knows which average to use for speeds over equal distances, and that the plain average of 45 would have been wrong.
How it is computed
n / Σ (1 / x)Where you see it
STATS_DESCRIPTIVE— Column-wise descriptive statistics with flexible metric selection and optional column filtering.
Related values
- 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.
- 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.
Get it in your sheet
One formula in a cell gives the whole report, Harmonic mean included. ALS Stats is a free add-on for Google Sheets™.
Install ALS Stats from Google Workspace Marketplace (opens in a new tab)