The Chiswick projectA Box-Cox transform for 3,109 building footprints
Measure every mapped building, see why the usual statistics fail, then find the scale on which they work.
We downloaded OpenStreetMap data for a rectangle around Chiswick and kept every closed building outline of at least five square metres: 3,109 of them. Python turns each outline into an area with the shoelace formula. The smallest is a 5.0 square metre outbuilding and the largest covers 21,588 square metres. The mean footprint is 212.6 square metres, but the median is only 95.3, and 82.6% of buildings are smaller than the mean. The largest 1% hold 22.6% of all the footprint area. The skewness is 18.09, where a symmetric bell curve would score zero.
Ordinary rules collapse on numbers like these. The standard deviation is 649.8 square metres, so "the mean minus two standard deviations" is minus 1,086.9 square metres, an area no building can have. The familiar outlier rule, anything more than three standard deviations from the mean, flags 36 buildings, every one of them large; it can never flag a small one, because there is no room below.
The same 3,109 footprints on different scales, our Python run on OpenStreetMap data| Scale | Skewness | Verdict |
|---|
| Raw area | 18.09 | Hopelessly lopsided |
| Square root | 5.13 | Better, still a long tail |
| Logarithm | 1.08 | Nearly there |
| Box-Cox, power -0.246 | -0.119 | Close to symmetric |
| Power -0.5 | -1.55 | Overshot: tail now on the left |
| Reciprocal (power -1) | -5.51 | Badly overshot |
Box-Cox treats the power as a dial and picks the setting under which the data look most like a bell curve. Here it chooses minus 0.246, a little stronger than a logarithm, and the skewness falls to minus 0.119. On the log scale the natural average is the geometric mean, 110.2 square metres, which sits close to the median and describes a typical Chiswick building far better than 212.6 does. The transform is no magic wand, though. On the new scale the three-deviation rule flags 38 buildings, 6 large and 32 small, so sheds and garages become visible as the oddities they are; and only 93.9% of buildings lie within two deviations, against the 95% a true bell curve would give. The tails are still heavier than the textbook shape, and an honest report says so.
Ages 8 to 11
Sort paper rectangles by size and see why "the average one" looks like none of them.
Ages 11 to 15
Compute footprint areas in Python and plot them on an ordinary and a log axis.
Ages 15 and up
Code the Box-Cox search, compare skewness by power and rerun the outlier rule.
Whose map, whose measurements
The building outlines are from OpenStreetMap, © OpenStreetMap contributors, under the Open Database Licence, read on 30 September 2026. They are what volunteers have drawn, which is not a survey of every structure, and outlines may be merged or missing. The areas, statistics and transforms are our own calculations.
