## Friday, 4 November 2016

### Average age

As I get older I find that I pay more attention to the ages of the people who appear each day in the obituary pages of The Times! Now I find that I have started to calculate the average (mean) age at which they died – and I am encouraged if it is greater than my age (it usually is!).

But, I have an interesting mathematical observation, related to the issue of rounding errors, to offer you.

Take this example. Four people are listed in the obituaries, dying at the ages of 69, 73, 76 and 80. What is the average (mean) age at which they died?

Now, 69 + 73 + 76 + 80 = 298. Divide this by 4 and we get 74.5 years.

But, this is NOT the average age of these four individuals.

Remember that when we say that someone died at the age of 69 this means that they could have been as little as one day short of their 70th birthday. Different conventions for rounding up or rounding down are used in various contexts. We always round down to the year below when we give someone's age in years.

So, the best estimate for the average age of the four individuals in this example would be the mean of 69.5, 73.5, 76.5 and 80.5 years. And that gives the mean age as 75 years.

At my age, let me assure you, that extra half a year is quite significant!