To kick off National Blog Writing Month, here’s something I’ve been saving up for my more mathematically inclined readers — and also for anyone who does scientific computing. It’s a quick computational trick to come out of all the stuff I’ve been doing lately that is not writing blog posts.

Sometimes you have to calculate the standard deviation of a set of numbers. Although there are various definitions of the standard deviation, the usual way to do this in physics is

where \(N\) is the number of data points and \(x_k\) are the values. But this can be pretty inaccurate when the values themselves are much larger than the variance — you wind up taking a difference of two very large numbers, the two terms under the square root, and expecting to come out with a small result. That’s bad. Sometimes the difference even winds up being negative!

There’s a better method, described on John D. Cook’s website: instead of computing two large …