MARCUS DU SAUTOY:'With the world's fish stocks under pressure, 'it's vital for us to find out as much about their populations 'as we possibly can.
MARCUS DU SAUTOY:'But with so many fish out there, it seems an impossible task.
MARCUS DU SAUTOY:'Yet using mathematics, 'I can discover things about the inhabitants of our oceans, 'without even getting my feet wet.'
SAM BRENCHLEY:I started fishing in Brighton in 1972. I've been a fisherman for 40 years, catching dover sole.
SAM BRENCHLEY:That's the main target species for the English channel.
MARCUS DU SAUTOY:'Each time he goes out fishing, 'Sam Brenchley catches Dover sole of all different shapes and sizes.
MARCUS DU SAUTOY:'And by tapping into the power of mathematics, 'I can predict a weight for the largest fish 'Sam's caught in his entire career. 'And all I need to do is get my hands on today's catch.'
MARCUS DU SAUTOY:That's 180 grams.
MARCUS DU SAUTOY:'Even though I've only got a handful of fish, 'their weights will give me all the information that I need 'for my prediction.'
MARCUS DU SAUTOY:Now using these numbers, I can calculate that the largest one should be about 1.3kg, which is roughly 3lbs.
MARCUS DU SAUTOY:'I've not weighed a single fish anywhere near that size. 'So let's see if I'm right.'
MARCUS DU SAUTOY:So what's the largest Dover sole that you've caught in your career?
SAM BRENCHLEY:We call them doormats, the large ones
SAM BRENCHLEY:and you maybe get four or five a season. The largest I'd say was 3 to 3.5lbs.
SAM BRENCHLEY:It's always nice to catch big stuff, you know? Well I think it is anyway.
MARCUS DU SAUTOY:'So without ever getting my hands on one of these giant doormats, 'just how did I work it out?'
MARCUS DU SAUTOY:Now the reason this calculation is possible, is because the distribution of the weights of fish, in fact, the distribution of lots of things like, the height of people in the U.K. or I.Q., is given by this formula.
MARCUS DU SAUTOY:'This is the normal distribution equation, 'and it's one of the most important bits of mathematics 'for understanding variation in the natural world. 'And it describes the shape of a graph 'that pops up time and time again throughout nature. 'The Bell Curve.
MARCUS DU SAUTOY:'The area under the curve represents all the fish Sam's ever caught.
MARCUS DU SAUTOY:'Most of them will be an average size.
MARCUS DU SAUTOY:'The small tiddlers, and large doormats are much less likely.
MARCUS DU SAUTOY:'To put values to this graph, I just need two bits of information. 'The mean shows me where the centre of the bell curve lies. 'And the standard deviation shows me the range of the weights.
MARCUS DU SAUTOY:'I approximated both of these just by weighing Sam's catch.
MARCUS DU SAUTOY:'Together they allow me to estimate values 'for all the fish he's ever caught, 'from the smallest to the largest.
MARCUS DU SAUTOY:'Knowing the weight of Sam's largest fish 'might not seem important,
MARCUS DU SAUTOY:'but this technique allows us to discover things 'about all manner of populations by measuring just a small sample.
MARCUS DU SAUTOY:'And from biology to medicine, and even engineering, 'the bell curve gives us the power to make predictions 'about our world and everything in it.'
Marcus du Sautoy examines a sample of dover sole from a day's catch, and by measuring the weight of this small number of fish, explores how the bell-curve of the Normal Distribution allows us to predict what the largest fish in the population is likely to weigh, even without catching it.
The calculations are not shown in full detail, but his prediction is backed up by a conversation with a fisherman.
This clip is from the series The Code.
Teacher Notes
Use as a practical example when looking at standard deviation and measures of location / measures of spread.
Would also work well as part of the Statistics GCSE course too.
For those who won’t be doing the actual calculation, students can still explore how the chance of getting a certain measurement changes with the number of standard deviations away from the mean.
Students can collect continuous data of their own – for example, heights of students in a particular year – and see if it fits this model.
Curriculum Notes
These clips will be relevant for teaching Maths at KS4 and GCSE in England, Wales and Northern Ireland and National 4/5 or Higher in Scotland.
The topics discussed will support OCR, Edexcel, AQA, WJEC in England and Wales, CCEA in Northern Ireland and SQA in Scotland.
