Measure at the percentile that hurts

A mean response time of 180ms is compatible with 5% of requests taking four seconds, and it is the 5% who write in. The average is the one number that cannot show you a problem affecting a minority.

# p50 120ms  p95 340ms  p99 3.9s
#
# the p99 is the interesting one: something is 30x slower
# for one request in a hundred, and the mean hides it

A p99 far from the p95 usually means a specific path rather than general slowness — a cache miss, a customer with far more data than anyone else, or a lock. That makes it diagnosable rather than a tuning exercise. Alert on p95 and investigate p99; alerting on the mean produces a number that only moves once the problem is universal.