When we measure the average experience, it's crucial what we are sampling/measuring uniformly to construct that experience.

The service provider is choosing to weight all requests uniformly, and average over requests -- some have 10s latency and some have 1s latency.

The user lives in time, and chooses to weight their time intervals equally. So a 10 second pause carries 10 times more weight for them than a 1 second pause -- because they experience it 10 times as much! So their average experience is a different weighted average.

The conceptual point is that averaging always needs a measure, and implicitly assumes one if you aren't explicit about the choice.