Trout, Catfish and Roach (and how to count fish and non-fish)

Author: Julian Champkin

How do you find out how many fish there are in a pond? There is a nice little booklet just published to tell you exactly that. It is called Trout, Catfish and Roach, it is illustrated with cartoons, and it starts like this: (If you have never wanted to count fish, hang in there for a bit please. Other things will be revealed.)

How do you find out how many trout there are in your pond?

You could drain it and count the fish I suppose, but it wouldn’t do them much good. Perhaps if the pond was small you could try and catch them all. That would take a while. But there’s nothing like fly fishing, so you decide to give it a go. At the end of day one, you’ve caught 100 trout. Pretty good!

So how many are there in total? Still no idea, really. So you tag each one, put them all back (you’ve lovingly cared for them all of course), and carry on the next day. The next day you manage to catch another 50; 25 with a tag, 25 without. So you’ve found another 25 and know for sure there are at least 125. Pretty good. That’ll have to do.

But is that all you’ve found out?

Half of those you caught on day two already had a tag. Does that mean half the trout in the pond were tagged on day one? Roughly, yes. And as you know you tagged 100 on day one, if half the trout in the pond were tagged, you can estimate that there must be around 200 in the pond altogether. Give or take a few.

The idea is simple when you take it step by step, but the implications are profound. You’ve only ever seen 125 fish in total, but can estimate with a fair degree of confidence that there are 75 or so more.

And so it goes on. The marginal surprise is that the book is published by the Office for National Statistics as part of the 2011 Census effort. Has the Office for National Statistics gone mad, I hear you cry? Have they added fish-counting to their day-job of counting how many people there are in the land? Not exactly. Trout, Catfish and Roach is their attempt to explain in clear English what exactly the 2011 Census was trying to do and how exactly it set about doing it. It sticks to the fishing analogy throughout. For example, catfish are harder to catch than trout, so you might imagine you have fewer of them in your pond; and some people – the homeless, for example - are harder to track down for a census, so you might imagine there are fewer homeless people that in fact there are.

The booklet’s subtitle is ‘The beginner’s guide to census population estimates’ but they have sensibly put that in small type that is easy to miss, so it need not put anyone off. It is short, it is simple, it is clear; and yesterday (June 29th) its author, Peter Benton won a commendation in the ‘Excellence in Official Statistics’ awards given by the Royal Statistical Society. Official statistics that are clear and easy to read are few and far between and deserve all the encouragement they can get. Trout, Catfish and Roach is available in booklet form (it would be ideal for teaching children) by e-mailing census.communications.team@ons.gsl.gov.uk, or you can download it for free as a pdf from here.

(And if you happen to have a pond, you could also use it to find out how many trout, catfish or roach are living in it. Happy fishing…)