Benford's law in UK data: a maths EPQ idea
A title to start from
Does Benford's law hold for UK data sets, and could it detect made-up numbers?
Why it works as an EPQ
A surprising law with a logarithmic explanation, and public data to test it on.
Scope and difficulty
Solid. Solid. Three or four data sets and one test of fit.
The maths
Builds on these A Level topics: Exponentials and logarithms · Hypothesis testing · Sampling and data.
You would learn:
- Why first digits follow log₁₀(1 + 1/d)
- Chi-squared goodness-of-fit (Further Statistics)
- Scale invariance
One possible plan
- Explain the distribution and why it arises from data spread over orders of magnitude.
- Test it on several public data sets.
- Make up numbers yourself (or with consenting friends) and test those.
- Judge when the law is and is not a fair test for fraud.
Pitfalls
- Applying it to data with a narrow range, such as heights.
- Calling a mismatch proof of fraud.
Where to start reading
- Search for: Benford's law explanation scale invariance
- Office for National Statistics data sets
Similar ideas
- Shared birthdays in real classesHow likely are shared birthdays in real classes, given that births are not spread evenly through the year?
- Why do opinion polls miss?Why do opinion polls sometimes get UK general elections wrong?
- Simpson's paradox in real dataWhen can combining groups of data reverse a conclusion, and how should we decide which answer is right?
- Does sacking a football manager work?Does sacking a football manager improve results, or is it regression to the mean?
All statistics and data ideas · all 93 ideas
Your EPQ must be your own work. These pages coach: ideas, structure, checklists and planning. Submitting text, proofs, code or analysis written by someone else or by an AI tool as your own is malpractice. How to use help and AI honestly.