1.4

## The University of Sheffield

Skip to 0 minutes and 9 secondsIn the last step, we looked at how apparently big numbers might not still seem so big when you take into account things like time. In those examples, and others like them, time is probably the most important thing to take into account. How many times will you be paying this sum of money? But in other cases, there are other things to take into account as well. In this step, we'll look at how numbers can be stripped of important context that help to inform you whether they're big numbers or not. Does 0.1% sound like a big number? Probably not.

Skip to 0 minutes and 44 secondsIf you told me something about 0.1% of people who live in Sheffield, I have a sense of how many people that is, because I know the size of the city. If you told me something about 10% of the food I eat in a week, I can guess at that. If you told me that 0.1% of people who took a flight between London and Hong Kong between 1990 and 1998 ate a specific dish in-flight, and asked me to guess how many bread rolls that meant the caterers had to bake, I would have no idea if that's a lot of bread rolls or not, because I don't have that sort of information at my fingertips.

Skip to 1 minute and 18 secondsThis kind of context is crucial in understanding whether numbers are big or not. 2% might sound like a small number of people, but if it's of all people in the world, it's a lot. 80% might sound like a lot of people, but if it's people who work in my building, its a lot less. How might this work in practise? Let's look at an example. There's been debate in the UK recently about the country's military spending. NATO has a target for its member states, of which the UK is one, to spend a minimum of 2% of their GDPs on defence. The UK has done so ever since it's been a member of NATO.

Skip to 1 minute and 54 secondsBut recent budget projections suggested it might fall short in the future. Once again though, it's important to consider whether 2% is a lot. At face value, 2% doesn't sound like a lot. It's a small fraction of GDP. In the financial year 2014-15, the UK spent £36 billion on defence, which was 2.2% of GDP. If the spending had been exactly 2%, the overall spend would have been 10% less. Unless you have overall GDP figures at your fingertips, £36 billion sounds like a lot more than 2%. As well as this, when we think about defence spending as 2% of something, we're comparing defence spending with the country's entire gross domestic product, rather than the amount that country spends.

Skip to 2 minutes and 47 secondsDefence spending as 2% of GDP is different from defence spending as 2% of overall spending. Going back to the year 2014-15, overall government spending in that year was about 43% of GDP. That means that the spending of £36 billion, or 2.2% of GDP on defence, corresponds to 5.1% of government spending. So in order to understand if spending 2% of GDP on defence is a lot, we need to understand how much money this is in total, and what fraction of government spending it corresponds to, in order to compare defence spending with other government spending.

Skip to 3 minutes and 31 secondsSo not only can 2% sound like a little or a lot, it can also be legitimate to describe this very same number as 5.1%, which obviously sounds like a little more than two and a half times as much. In order to make sense of data in the media, when we see percentages quoted, we should be asking, as a percentage of what? But also, how much does 100% actually correspond to, whether that 100% is a number of people, a sum of money, or something else.

# How much of what?

Does 0.1% sound like a big number? Stripped of important context, it’s almost impossible to tell.

Context is crucial in understanding whether numbers are big or not, particularly when it comes to percentages. 2% might sound like a small number of people, but if it’s of all people in the world, it’s a lot; 80% might sound like a lot of people, but if it’s of the people who work in your office; it’s a lot less. Whenever we see percentages quoted, we should be asking “as a percentage of what?”, “how much does 100% actually correspond to?” and “what is 100%; a number of people, a sum of money, or something else?”.

In this video, Mark demonstrates how numbers can look big or small in relation to the whole ecosystem in which they sit.

In your experience, are these techniques more or less common than the ones discussed in the previous step?

### References

Frances Perraudin (2015). Defence spending: MPs vote in favour of keeping budget at 2% of GDP. The Guardian online [Accessed 3 Feb. 2016]

Stockholm International Peace Research Institute, SIPRI Military Expenditure Database. online [Accessed 3 Feb. 2016]