One in Five, One in Six, Whatever

It’s a boring time of the year so any news is eagerly seized upon, particularly if it seems good. On 30 December 2010 the BBC ran a story, Nearly one in five UK citizens 'to survive beyond 100':

Nearly one in five people currently in the UK will live to see their 100th birthday, according to the government. The Department for Work and Pensions (DWP) said its figures suggested 10 million people - 17% of the population - would become centenarians.  These are based on Office for National Statistics population projections and life expectancy estimates.”

But hang on, the headline in the Daily Mail next day was One in six will live to be 100, although their article quoted the same 17%. Other reports were also divided between “one in five” and “one in six”.

This was largely a fractions vs percentages problem: 17% is nearly 20% which is one in five, isn’t it? – No, and see attempt-to-be-helpful table below – but it is also worth following the story back.

The DWP press release said, “More than ten million people in the UK today can expect to live to see their 100th birthday – 17 per cent of the population”, which was picked up by the media. This statistic came from a DWP report, Number of Future Centenarians.  DWP’s interest is, of course, how to find pensions for all these people, and they based their analysis on the ONS projections. As usual, the underlying caveats get lost sight of:

... the population levels and age structure that would result if the underlying assumptions about future fertility, mortality and migration were to be realised. Projections are uncertain and become increasingly so the further they are carried forward.

I wonder whether the assumptions about future mortality are taking current trends in obesity (and consequently Type 2 diabetes etc) into account.  Apart from that, it is informative to go into the statistics in the report. The source of the 17% is this data:

So the 17.3%, correctly reported as “one in six” rather than “one in five”, is an average for males and females. However most of us are one or the other, and for females 20% (19.98%) is almost exactly “one in five”, but for males 14.5% is, alas, more like “one in seven”.

Of course, we’re not only broken down by sex, but by age as well. A one-year old female in 2010 is considered to have a 32.8% (1 in 3) chance of reaching 100, but a male of Western Independent’s age has only a 1 in 12 chance. So read this blog regularly while it lasts!

(for percentages with one decimal place and rounding to smaller fraction)