Here's a totally misleading chart from the BBC website, supposedly showing the relative numbers of Anglicans and Catholics in the UK and Ireland compared to the population as a whole.
Wow! Look at that! The Anglicans are over half-way up the chart when compared with the whole population, and the Catholics over a third of the way up. Not bad!
Until you realise that it is the areas of the semi-circles we should be looking at, not the diameters. The clue's in the figures given in the labels on the chart (which totally misleadingly point to the semi-circles' diameters): 65.6M population, 9.3M Catholics—that's one in seven a Catholic, not one in three. 65.6M population, 26.5M Anglicans—that's 40% Anglicans, not over 50%. But who's going to check the figures when there's a simple, reassuring chart? Apart from me, I mean.
And, to make matters worse, they've overlaid the semicircles. Or have they? How are we supposed to know if it's just the yellow area which represents the proportion of Anglicans, or if it's the total of the yellow and red areas? (I have calculated the areas, so I believe it's the latter.)
Actually, it's even more misleading than that. Think of the chart as being like a Venn diagram: Anglicans are indeed a subset of the entire population of the UK and Ireland, as are Catholics, but Catholics are most definitely not a subset of Anglicans. In fact, you could argue that the exact opposite is true: historically, the original Anglicans were a subset—or, rather, subsect—of the Catholic Church. And some of them might soon be again, according to the BBC article.
Setting aside the question of what counts as a Catholic or Anglican (I am a devout Atheist, but I was christened against my will by the Anglican church, so does that make me an Anglican?), and setting aside the fact that the church membership figures quoted were provided by the Catholic Church and the Church of England (who might be a little bit biased), this chart seems designed to give a misleadingly high impression of the churches' memberships. It would be interesting to know whether the BBC just obtained the figures from the churches, or whether they obtained the chart as well.
I have banged on previously about how 3-D pie charts can be misleading, but I find these overlaid semi-circular charts far more obnoxious. What on earth is wrong with showing a simple, 2-D pie chart?