Variability in software runtime arises mostly from other software running on the same system.

If you are looking for a real-world, whole-system benchmark (like a database or app server), then taking the average makes sense.

If you are benchmarking an individual algorithm or program and its optimisations, then taking the fastest run makes sense - that was the run with least external interference. The only exception might be if you want to benchmark with cold caches, but then you need to reset these carefully between runs as well.