Standard deviation classification
A way to group data into classes for a map by how far each value lies above or below the average, measured in standard deviations.
Standard deviation classification does not ask how high a value is, but how far it is from the average. It calculates the mean of all values and the standard deviation, a measure of how widely the values spread around that mean. The class breaks then sit at the mean and at steps of one standard deviation, or a fraction of one, above and below it.
Take ten areas with these values: 38, 44, 47, 49, 51, 52, 54, 56, 59 and 70. The mean is 52 and the standard deviation is about 8.3.
| Class | Range | Areas | Values |
|---|---|---|---|
| More than 1 SD below | under 43.7 | 1 | 38 |
| Up to 1 SD below | 43.7 to 52 | 4 | 44, 47, 49, 51 |
| Up to 1 SD above | 52 to 60.3 | 4 | 52, 54, 56, 59 |
| More than 1 SD above | over 60.3 | 1 | 70 |
The map that results answers one question well: which areas are unusual. Most areas fall in the two middle classes, and the ones that differ clearly from the average stand out at both ends. It works best with a diverging palette, two colours that meet at a neutral middle value, so that below average and above average read as opposites.
The method assumes the values spread roughly evenly around the mean. With skewed data, such as many low values and a few very high ones, the mean is pulled up, the lower classes can start below zero, and the map says more about the outliers than about the pattern. The legend should also show real values, not only “1 SD above”, because few readers think in standard deviations. In GOAT, standard deviation is one of six methods in attribute-based styling.