The Grimsby projectSynthetic workers from two census tables
Generate data that match every published total, then read the individual records.
The learner downloads two tables for the borough. One splits 68,850 working residents by method of travel: 41,180 drivers, 6,360 on foot, 3,423 by bicycle, 9,605 mainly at home, and so on. The other splits 68,849 by distance travelled. The totals differ by one person, because the census adds small privacy noise to each table separately. Using Python's random module with a fixed seed so the run can be repeated, the program creates 68,850 synthetic workers, choosing each one's method and distance by the shares in the two tables. Count them up again and the proportions match the census almost perfectly. By the usual summary checks, this looks like excellent training data.
Implausible records among 68,850 synthetic North East Lincolnshire workers, our Python run, 28 September 2026| Check | Methods drawn independently | With a home-working rule |
|---|
| Home working in one field but not the other | 16,446 (23.9%) | 0 |
| On foot, 60km and over | 124 | 132 |
| By bicycle, 60km and over | 76 | Not re-counted |
| On foot, 20km or more | 460 | 547 |
| Driving under 2km | 6,848 | Plausible, kept |
Reading actual rows tells a different story. Because method and distance were drawn separately, 16,446 synthetic people, almost a quarter, work mainly from home according to one field while commuting some distance according to the other, or the reverse. The learner checks that against a quick calculation: independence predicts about 16,530, so the program is behaving exactly as designed. The design is the problem. There are also 124 people who walk 60 kilometres or more to work every day, and 76 who cycle that far. None of these break the published shares.
The first fix is a rule: anyone who works from home in one field must do so in the other. That removes the contradiction completely, but the long-distance walkers remain, 132 of them in the second run, because the two tables never say how method and distance relate. That information lives in the joint distribution, a cross-table of method by distance, which the learner would need before generating realistic records. The conclusion is the valuable part: synthetic data can match every summary and still be nonsense record by record, and a model trained on it would learn that walking 60 kilometres to work is normal.
Ages 8 to 11
Make "people cards" by picking a travel method and a distance from two hats, and spot the silly ones.
Ages 11 to 15
Generate synthetic workers in Python and write checks that flag impossible pairs.
Ages 15 and up
Compare independent sampling with rule-based fixes and explain why joint data are needed.
Census tables, our synthetic records
Counts come from the Census 2021 tables TS061 and TS058 on Nomis. Every synthetic worker, check and count in the table above is our own work.
