Sig Figs

I work with climate data, most usually sea-surface temperature data. I say “climate” data, but lots of the historical measurements weren’t made with future climatologists in mind. They are – it is safe to say – of variable quality, and the principal challenge of working with this kind of data is understanding how reliable they are. It is a significant challenge.

From time to time, people offer advice and share the fruits of their experience with the climatologists to ease their struggle with this difficult task. Whenever I see a blog post or thread on the subject of historical sea-surface temperature (or historical any data for that matter), I always read it. There’s a whole world of experience out there – experts from different branches of science, engineers, technicians, people who work with figures every day – and there is, I figure, a chance that someone will say something that is helpful. If they don’t there are usually a few good anecdotes about the shenanigans that bored sailors indulge in.

Mostly though, there’s little that’s new (apart, perhaps from the perverse ingenuity of sailors in the pursuit of anything other than boredom). One sees the same arguments repeated over and over again. One that keeps coming up, is this one:

Advertisement

The same thing lots of times or lots of things one time

Tags

uncertainty

There is a myth (like this one, but different) that averaging together multiple measurements can only reduce uncertainty in one very specific circumstance: when all the measurements are of the same thing.

I want to show, simply, that if you can reduce the uncertainty of an average in that particular case then there are situations where you can reduce the uncertainty in any average, even when the measurements are of different things.