Q: Why are latency percentiles (P50, P95, P99) more useful than average (mean) latency for understanding user experience? Give a concrete example where average is misleading.

Average latency is deceptive because it hides the temporal distribution of requests. A system can have a "good" average while users experience terrible performance.

• 100 requests: 99 complete in 10ms, 1 takes 10,000ms (user hits a database lock or GC pause).
• Average = (99×10 + 1×10,000) / 100 = 109ms (looks acceptable)
• P99 = 10,000ms (the 1% percentile experiencing the lock, which is unacceptable for a web app)
• P50 (Median): Half of users experience better, half worse.

Concrete example: Why percentiles matter: For SLOs, you never use average. You commit to "P99 latency < 200ms" because that's a user experience promise. Tail latency (P99, P99.9) is the metric operations teams care about.

• P95: 95% of users are fast. If P95 is 200ms, the slowest 5% experience delays.
• P99: Only the slowest 1% suffer. If P99 is 5 seconds, you're losing at least 1 in 100 users.