I've just been doing some online research looking at statistics for the proportions of people who say they believe in God, or not. As a committed Christian believer, this subject is obviously of some interest to me. I came across this report in the Guardian (11 October 2010):

*A report for the Church of England last week suggests that for many young people in the UK, Christianity is no more than a "faint cultural memory". A minority are explicitly atheist – about one in eight – and around four times as many believe in either a personal god or a vague higher power. But by far the largest category are those who just find the question bewildering and not very interesting: "I don't really know what to think" got 43% of the answers.*

This is a typical example of reporting where the reported statistics just do not add up!

(a) 'About one in eight' are explicitly atheist. That's about 12.5%.

(b) 'Around 4 times as many believe ...' So, that's about 50%.

(c) Which leaves only 37.5% for the third category of response - but this is reported as 43%.

If this 43% is correct, the discrepancy might be explained as the result of compounding two rounding errors.

'About 1 in 8' could be a proportion somewhere between '1 in 7.5' (13.3%) and '1 in 8.5' (11.8%).

So, assuming the smallest proportion that might count as 'about 1 in 8', we could have 11.8% in category (a).

This means the most we can have in category (b) is 100% – 43% – 11.8% = 45.2%. And this would be acceptably described as 'about 4 times' the proportion in category (a) – it is about 3.8 times.

But unfortunately, the report told us that (c) was by far the largest category. And 45.2% is larger than the 43%!

I just cannot find any way in which all the statistical statements in this report can be correct.

Why did the reporter not just give us the straight percentages?

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