# A Fermi Estimation Problem: How Many People Have A Maths A-Level?

In an idle moment, I wondered how many people in the UK ((Rather, England and Wales)) have an A-level in maths.

This strikes me as a great Fermi estimation question – you can come up with any number of answers and bounds on it and probably nobody knows the answer even roughly. (You might be able to get the number of A-levels *awarded*, but some recipients will no longer be with us.)

### Some wide bounds

Somewhere in the back of my head, I know that about 100,000 people took A-level maths last year. And that feels about right – if there are 40,000,000 in England and Wales, that works out as about 500,000 18 year-olds (give or take), and 20% of them taking maths doesn’t seem like a huge stretch. So: at least 100,000 A-levels are almost certainly out in the wild, and that’s a (very low) lower bound. We could say the numbers have been pretty stable for the last half-decade or so and bump it up, but let’s stick with it.

A-level numbers have been going up, and it’s likely that 100,000 is about the biggest cohort ever. A-levels were introduced in 1951, so there’s about 70 years available – making 7,000,000 a (very generous) upper bound.

### A good start

That’s already a good start: more than 100,000 and less than 7,000,000 suggests “about a million” as a reasonable ballpark answer straight away. But can we do better?

Probably.

I would probably model the A-level uptake as a straight line, rising steadily from “not very many” in the 1950s to today’s numbers – that would suggest a number around 3,500,000. I suspect that’s an overestimate and that “two or three million” is a reasonable number, about 5% of the population.

How would you approach it? Do you get a different answer? I’d love to hear about it!