Median also lies more than 99th/100th percentiles because in many workloads the same client is making multiple parallel requests and often waiting for the slowest.
See this piece from Jeff Dean [0]
Quote:
""" Component-Level Variability Amplified By Scale
A common technique for reducing latency in large-scale online services is to parallelize sub-operations across many different machines, where each sub-operation is co-located with its portion of a large dataset. Parallelization happens by fanning out a request from a root to a large number of leaf servers and merging responses via a request-distribution tree. These sub-operations must all complete within a strict deadline for the service to feel responsive.
Variability in the latency distribution of individual components is magnified at the service level; for example, consider a system where each server typically responds in 10ms but with a 99th-percentile latency of one second. If a user request is handled on just one such server, one user request in 100 will be slow (one second). The figure here outlines how service-level latency in this hypothetical scenario is affected by very modest fractions of latency outliers. If a user request must collect responses from 100 such servers in parallel, then 63% of user requests will take more than one second (marked “x” in the figure). Even for services with only one in 10,000 requests experiencing more than one-second latencies at the single-server level, a service with 2,000 such servers will see almost one in five user requests taking more than one second (marked “o” in the figure).
"""