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## The University of Sheffield

Skip to 0 minutes and 10 secondsWhat's a big number? This might sound like a silly question, but if we want to make sense of data in the media, then whenever we hear numbers quoted, one of the first things we should be asking is whether those numbers are big numbers or not. If a number sounds big at first, it doesn't necessarily follow that it's actually a big number, nor does it follow that a small sounding number is actually a small number. There's lots of things to think about in order to make the decision. Sums of money are often big sounding numbers, and big sounding sums of money tend to be impressive sounding sums of money.

Skip to 0 minutes and 45 secondsIf you want to make an amount of money sound impressive or like a big number, a straightforward way to do this is to ignore how many people you're spending money on, and how many times bits of the sum of money gets used. Let's look at an example of how this might work in practice. In the UK, a scheme has been running for the last few years called the PE and Sport Premium in order to increase the quality of physical education for pupils up to the age of 11. In 2014, there was an announcement that the government was spending £150 million extra on school sports.

Skip to 1 minute and 22 secondsBut in order to understand if that's a lot, we need to look at the number in context. The first important piece of context is that this bit of funding was scheduled to be £150 million per year over a period of three years. So the total sum of money committed was £450 million. This big number is starting to look even bigger. However, the second important piece of context is the number of schools the money's being spent on. There's about 16,000 schools in Britain with pupils up to the age of 11. So we should look at the amounts of money being spent on each primary school. This is about £9,000 per school per year.

Skip to 2 minutes and 4 secondsBut we don't only have to look at how much money's being spent per school, we can also look at how much money's being spent per pupil. Let's simplify things by imagining that all of these schools have the same number of pupils each. The average is about 250 pupils per school. This means that the big number corresponds to about £36 per pupil per year. And we've already looked at how the big number refers to an amount of money per year. What about per week? Pupils up to 11 spend 39 weeks in school per year. So we can divide this big number up, yet again, to see how much money is spent per people per week. This is about 92p.

Skip to 2 minutes and 49 secondsSo, we started at what sounded like a big number at £150 million across the whole primary school system. This works out at about 92p per pupil per week, which sounds a lot smaller. This can work the other way as well. If someone is spending money on you, they're likely to want to make it sound as impressive as possible. On the other hand, if someone wants you to spend your money on them, it makes sense for them to try to make the money sound as small as possible. After all, you'd rather spend less money than more money on the same thing. This can be done by just reversing the process from before.

Skip to 3 minutes and 28 secondsHow widespread this kind of practice is will depend on where you live, and what sorts of people and organisations are trying to persuade you to spend your money, but there's one sector in one country where this comes up a lot. Here's an example. While numbers that appear big are often used to impress us, numbers that appear small are often used to seduce us and can begin to get a lot bigger before very long. In order to put these numbers into context, we can use some of the same techniques as before, but in reverse. One setting when numbers might be used to seduce us is when advertisers are selling products to us.

Skip to 4 minutes and 6 secondsIf prices can appear small, we might be more likely to buy the thing that's being offered. A clear example of this phenomenon is car sales. For many people, cars are among the most expensive purchases that they ever make, and when people are deciding what to buy, it's important to understand how expensive each option is. In order to do so, those decisions need to be made with comparable figures for each option. In some countries, this is relatively easy. There's a sticker on a car with a number, and that number is what it costs to buy the car. In other countries, though, things are more complicated with the number on the sticker being the amount you have to pay per month.

Skip to 4 minutes and 51 secondsIn order to compare the two different stickers, the purchaser needs to get from the price per month to the overall price. The first step is to see how many times you have to pay the amount on the sticker. It's common to have to pay this amount each month for a period of three years. So a sticker price of $659 per month invokes paying$23,724 over a period of three years. The second step is to see whether there any other costs. Is it just a case of paying this amount each month? Often there's an additional upfront fee as well, similar to a deposit. In this case, that some is \$4,954. And that's just what's made explicit.

Skip to 5 minutes and 40 secondsThere's other costs as well as in this example. So the number we saw at the start was not very large compared with the overall amounts of money it costs to buy and to keep this car. This is a clear case of a large number being made to look smaller by chopping it up into small parts. So, it should be clear that just because something sounds like a big number, it doesn't follow that it's a big number. And if something sounds like a small number, that doesn't mean that it's a small number.

Skip to 6 minutes and 10 secondsThese tools are used by governments, advertisers, and by all sorts of other organisations in order to encourage people to change their perspectives in particular ways, and to tell particular stories. These are then often reproduced in the media, and if you want to make sense of data in the media, it's important to be conscious of these tools.

# What is a big number?

It may sound like a silly question, but if we want to make sense of data in the media, then whenever we hear numbers quoted, one of the first things we should be asking is - is that a big number?

If someone’s spending money on you, they’re likely to want to make that figure sound as impressive as possible; on the other hand, if someone wants you to spend your money on them, they’ll want to make that figure sound as small as possible.

In this video, Mark explains some of the ways that big numbers can be made to sound small and small numbers can be made to sound big.

Do these techniques sound familiar to you? Do you know of any similar techniques that haven’t been mentioned here?

### References

Department for Education and Edward Timpson MP, (2014). £150 million to boost primary school sport. online [Accessed 3 Feb. 2016].