Benford’s Law is a very powerful and counter-intuitive mathematical rule which determines the distribution of leading digits (ie the first digit in any number). You would probably expect that distribution would be equal – that a number 9 occurs as often as a number 1. But this, whilst intuitive, is false for a large number of datasets. Accountants looking for fraudulant activity and investigators looking for falsified data use Benford’s Law to catch criminals.

The probability function for Benford’s Law is:

This clearly shows that a 1 is by far the most likely number to occur – and that you have nearly a 60% chance of the leading digit being 3,2 or 1. Any criminal trying to make up data who didn’t know this law would be easily caught out.

Scenario for students 1:

You are a corrupt bank manager who is secretly writing cheques to your own account. You can write any cheques for any amount – but you want it to appear natural so as not to arouse suspicion. Write yourself 20 cheque amounts. Try not to get caught!

Look at the following fraudualent cheques that were written by an Arizona manager – can you see why he was caught?

Scenario for students 2:

Use the formula for the probability density function to find the probability of the respective leading digits. Look at the leading digits for the first 50 Fibonacci numbers. Does the law hold?

I’ve put together four comprehensive pdf guides to help students prepare for their exploration coursework and Paper 3 investigations. The exploration guides talk through the marking criteria, common student mistakes, excellent ideas for explorations, technology advice, modeling methods and a variety of statistical techniques with detailed explanations. I’ve also made 17 full investigation questions which are also excellent starting points for explorations. The Exploration Guides can be downloaded here and the Paper 3 Questions can be downloaded here.

All content on this site has been written by Andrew Chambers (MSc. Mathematics, IB Mathematics Examiner).

New website for International teachers

I’ve just launched a brand new maths site for international schools – over 2000 pdf pages of resources to support IB teachers. If you are an IB teacher this could save you 200+ hours of preparation time.

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December 27, 2016 at 6:31 am

RogerExcellent. Couldn’t remember the name, found the site by accident. It’s great, reminds me of Tom Murphy’s ‘do the math’ site.