I’m not sure what’s customary in most places, but in my experience you base most things off of avg and p99 and then you can use other percentiles to interpolate the shape of the distribution in the event you need a better model (you usually don’t). Of course I’m sure this sort of thing varies wildly by use case.
I admit that I don't deal a lot with latency measurements, but my memory from working at Google was that we focused on p50, p95, and p99. That was six years ago, and it wasn't my focus there, so it's possible I'm misremembering (especially based on all the responses saying I'm the weirdo for expecting p50).
Looking at Google's SRE book, they use p50, p85, p95, and p99, so it's possible I'm misremembering or that Google uses unusual metrics:
