*This resource is part of the collection Should I Risk It?*

Watch the video below, where Prof David Spiegelhalter discusses a newspaper headline about eating bacon sandwiches.

So said the headlines.

Of course we're all used to newspaper headlines which aim to shock us with eye-catching numbers. But how worried should we actually be by statistics such as this?

What other information might you want to know to decide how worried you should be?

One important piece of information to know is that, amongst those people who don't eat bacon sandwiches, 5% will at some point get bowel cancer.

To make our calculations easier, we can use natural frequencies, where we consider what we expect to happen to 100 people.

Suppose there are 100 people who do not eat bacon sandwiches. We can represent the random 5% who get bowel cancer in a diagram like the one to the right.

Now, suppose these 100 people decided to eat a bacon sandwich every day.

The papers announced that eating a bacon sandwich every day increased the risk of bowel cancer by 20%.

Does your answer agree with Prof Spiegelhalter's calculations in the video?

If the 100 people did not eat bacon sandwiches, then we would expect 5 to get bowel cancer.

The newspaper headlines said that we would expect the number to increase by 20%. 20% is the same as $\tfrac 15$, so we would expect an extra one person out of the hundred to get bowel cancer.

The

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Why do you think that the newspaper decided to consider the relative risk, rather than the absolute risk?