# Multiple methods for computing percentiles

## 2008-02-13

A recent discussion on the Medstats group highlighted some of the confusion about computing percentiles. I use a simple formula. If you want the pth percentile of a set of n observations, select the p(n+1) value from the data. If p(n+1) is not a whole number then choose a value halfway between the two adjacent values.

Suppose for example, you have 8 observations and you want to compute the 25th percentile. The value of p(n+1) = 0.25(9) = 2.25. According to this method, you would select a value halfway between the second and third observation. If these values are 10 and 14, then percentile would be 12.

But there are some who argue that you should interpolate. This means that you choose a value a quarter of the way between the second and third observations. This would make the percentile 11 rather than 12.

When p(n+1) is not an integer, some suggest rounding the value down and choosing that value. In this particular case, the percentile would be the second observation (10).

Some people don’t add 1 before multiplying by p or add a smaller constant like 1/2 or 3/8. There are at least eight different methods that are commonly practiced.

There is little practical difference between these methods, and no strong theoretical reason to prefer any particular formula. It only serves as a source of confusion when one statistical program chooses a slightly different percentile than another program.

You can find an earlier version of this page on my original website.