From Covid claims to cocaine stats: why misleading numbers matter

Today is National Numeracy Day, and at Full Fact we often see how easy it is for figures to mislead, confuse or be misunderstood—sometimes by accident, and sometimes deliberately. From viral Covid claims to misleading headlines and honest mistakes, poor numeracy can often distort how we see the truth.

Towards the end of 2021, for example, as the very worst of the pandemic was passing, we began to see claims that most of the people dying of Covid had been vaccinated.

This was actually true. In late 2021, the majority of people who died from Covid had indeed been vaccinated. But was this a reason to worry about the vaccines, as some on social media suggested?

It was not. But the reason why not may be far from obvious. Because this was a trick of the numbers—sometimes called the “base-rate fallacy”. In fact, the vaccines made people much less likely to die of Covid. But by that time, so many vulnerable people had received them—more than 90% of the over-80s—that even the small proportion who succumbed outnumbered those who died without being vaccinated. The claim was shared widely across social media without this important context.

In 2022, to take another example, we noticed that the government’s National Insurance web page said that contributions “will increase by 1.25%”. If you saw that today, how much do you expect your NI bill to rise by?

For most people, it actually meant a rise in their bill of about 10%, because the government’s figure was a rise of 1.25 percentage points—from 12% to 13.25%, in other words. For some people that distinction will be obvious. For others, it could make the difference between a tax rise they hardly need to think about and another that they definitely do.

People do seem to struggle with percentages in particular. During the doctors’ strikes in 2023, it was often said by ministers and the media that junior doctors were demanding a pay rise of 26%. And you could see where this came from. The doctors’ union claimed that the value of their pay had fallen by 26%, and they wanted it restored.

But of course, a fall of 26% actually needs a rise of about 35% to return things to where they were before. (Take 26 away from 100 and you get to 74. But 26 is 35% of 74, so that’s the rise required to get back to 100 again.)

Often the simplest mathematical mistakes, and the largest, are just a matter of scale. In March, we saw outrage online that MPs were supposedly getting a pay rise of 28%. It was actually 2.8%, as we pointed out.

And a number of BBC radio bulletins informed the nation in April that Brits collectively consume about 117 million tonnes of cocaine every year. As we wrote shortly afterwards, we’re not sure how much cocaine the UK does consume, but we’re confident it’s not 117 million tonnes. That would be nearly two tonnes each. It turned out that the word “million” was somehow added to the National Crime Agency’s actual estimate by mistake.

At Full Fact, we’re always working to make the important numbers clearer and misinformation harder to spread. Explore our fact checks and explainers to see how we help make sense of the stats.