Tuesday, 16 August 2011

Back of the envelope calculation suggests 2/3 of over 65s can't be alive today

A current HSBC campaign makes the amazing claim that "Two-thirds of the people who have ever reached 65 are alive today".

The world's over 65s have gone from a mere 5% in 1950 to a staggering 8% by 2010.

credit: http://commons.wikimedia.org/wiki/File:Percentage_of_the_World_Population_Over_65_-_1950-2050.png

Meanwhile world population has increased from around 2.5 billion people to around 7 billion in 2010.

credit: http://www.census.gov/population/international/data/idb/worldpopgraph.php

Assuming that both of these trends are linear (which admittedly oversimplifies the age structure trend) we can easily work out the number of people over 65 who have died since 1950 once we have a suitable death rate. The CDC puts the current death rate for 65-74 year olds at 2.1% in the US.

Putting all this together gives us the following:

number of over 65s alive in 1950: 125m
number of over 65s alive in 2011: 560m

The equation for number of over 65s who died is simply a matter of summing up 2% of the over 65 population for each year between 1950 and 2010:

(125 * 0.02) * 60 + (((560 - 125) * 0.02) / 2) * 60

2.5 * 60 + 4.35 * 60 = 411 million over 65s died since 1950

From this we can see what percentage of people who have ever reached 65 (since 1950) are alive today:
560 / 971

= 57%

This would seem to make HSBC's campaign sound quite unlikely as we have the rest of human history to add people to the total. The figures are very rough here but it would take some bold assumptions to reach their total.

Thanks to Ed Yong for mentioning the campaign.

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