Ever since I took GCSE and A-Level statistics, I've had a healthy appreciation for the way they are presented to the public.

I vividly remember my grandmother shouting at the television one night. The news presenter had said "20% of people polled - that's nearly a quarter..." Before she could finish, my grandmother loudly interjected, "Nearly a quarter? It's exactly a fifth!"

The way people see, hear and understand statistics is very complex. It's a rich mine of study for economists, neuroscientists and anthropologists. Given its complexity, shouldn't we me making it as easy to understand as possible?

I'm going to show you a few poorly presented statistics from the BBC News site. I pick on the BBC only because it's the site I read most often. Other news services are just as bad.

BNP

There is much wailing and gnashing of teeth at the apparent bump in the polls the fascists got following their Grand Wizard's leader's appearance on Question Time. Here's how it's reported.

BNP support in poll sparks anger 🔗

The opinion poll carried out after Mr Griffin's appearance found 22% of voters would consider voting BNP in a future local, general or European election.

Two-thirds of the 1,314 people polled by YouGov for the Daily Telegraph dismissed voting for the party under any circumstances, with the rest unsure.

When asked how they would vote in an election tomorrow, the proportion supporting the BNP stood at 3%, up from 2% a month ago.

However, more than half of those polled said they agreed or thought when asked if the party had a point in speaking up for the interests of "indigenous, white British people".

I don't want to comment on the validity of the poll - but the way in which its results are presented make it really quite difficult to gain a quick understanding of the situation.

The stats are presented in four different formats.

• Numerical: "22%"
• Verbal: "More than half"
• Fractional: "Two-Thirds"
• Relational: "x% up from y%"

This means that within 4 paragraphs the user has to switch their mental model of how the statistics are represented 4 times.  It makes it hard to easily compare the statistics on offer.  It leads to confusion and, ultimately, ignorance of what is being reported.

In the above example, what percentage of people were "Unsure"?

Off the top of your head, is two-sevenths greater or less than 22%?  By how much?

Political Party X has seen its support drop by nearly a third to just over 40%.  What was the party's original level of support?

These head-scratchers become easier when expressed in a common base - or when set out graphically.

Florence Nightingale is credited with creating the Pie Chart in order to explain to non-statistical civil servants the problems she faced in the war. While Pie Charts have some usability problems, there's no reason why a suitable graphical representation of the numbers can't be shown.  It allows those less versed in numerical reasoning a chance to evaluate the data presented.

The joke at the top of the page is based on the classic Binary Joke.  It relies on your confusion between base-10 and base-2.  When you mix and match different ways of expressing statistics, you might as well be mixing binary, decimal, and hexadecimal.  When reporting on statistics, clarity is the key to comprehension.