There's an ongoing effort to introduce quantile() into numpy.  You'd use it just like percentile(), but would input your q value in probability space (0.5 for 50%):

Since there's a great deal of overlap between these two functions, we'd like to solicit opinions on how to move forward on this.

The current thinking is to tolerate the redundancy and keep both, using one as the engine for the other.  I'm partial to having quantile because 1.) I prefer probability space, and 2.) I have a PR waiting on quantile().