The Yeovil projectA variogram of Yeovil's hills
Take every pair of places, note how far apart they are and how different, and look for the pattern.
Ordnance Survey publishes the grid position of every postcode. The BA20 and BA21 districts, which cover Yeovil and some villages beyond its edge, contain 1,262 postcodes at 1,204 distinct points. For each point the learner asks an open elevation service for the ground height, taken from a European height model with a 25 m grid. The heights run from 22.4 m to 111.5 m above sea level, with a mean of 65.7 m. Then comes the big loop: all 724,206 possible pairs of points. For each pair Python records the distance between them and the difference in height, and sorts the pairs into distance bands.
Height difference between pairs of Yeovil postcode points, by distance apart (our Python run on OS Code-Point Open and EU-DEM heights)| Distance apart | Pairs | Average height difference |
|---|
| Under 100 m | 2,254 | 2.0 m |
| 100 to 200 m | 6,649 | 4.4 m |
| 200 to 300 m | 9,865 | 7.0 m |
| 400 to 500 m | 15,253 | 11.1 m |
| 750 m to 1 km | 52,570 | 17.3 m |
| 1 to 1.5 km | 116,428 | 22.4 m |
| 1.5 to 2 km | 123,439 | 26.8 m |
| 2.5 to 3 km | 90,623 | 24.0 m |
Across all pairs, whatever their distance, the average difference is 22.3 m. Neighbours under 100 m apart differ by only 2.0 m, a tenth of that. The difference climbs steadily with distance and reaches the all-pairs level at a little over 1 km. Statisticians plot half the average squared difference, called the semivariance, against distance; that plot is the variogram. Here the semivariance is 3.5 for the closest band and first passes the overall variance of the heights, 377.9, between 1.3 and 1.4 km. That distance is the range: beyond it, knowing the height of one place tells you nothing useful about the other. Past 2 km the figure drifts down again, which reflects the particular shape of these hills and the edges of the area, and is a reminder not to over-read the far end of the plot.
Why does this matter for AI? The learner builds the simplest possible predictor: guess a point's height from the nearest point whose height is known. Tested the usual way, by hiding a random fifth of the points, it looks superb, with an average error of 2.16 m. But the hidden points had known neighbours just 70 m away on average. Tested honestly, by hiding a whole 1 km grid square at a time so the nearest known point is further off, the error is 6.23 m, nearly three times worse. Guessing the mean height every time scores 16.47 m. The model did not change between the two tests; only the test did. One caution about the data: points closer together than 25 m can fall in the same cell of the height model, which makes the very shortest band look a little smoother than the ground is.
Ages 8 to 11
Mark heights on a paper map and compare next-door houses with houses across town.
Ages 11 to 15
Loop over pairs of points in Python, bin them by distance and chart the average difference.
Ages 15 and up
Compute the semivariance, read off the range, and compare a random test split with a block split.
Data and licences
Contains OS data (C) Crown copyright and database right 2026 (Code-Point Open, Open Government Licence). Heights are from the EU-DEM model, served by OpenTopoData, read 30 September 2026. Distance bands, averages and the two tests are our own calculations. A postcode point is a position for a group of addresses, so these are heights at postcode points and no survey of any property.
