Percentiles, quartiles and ranks
The mean and the median describe the center of the data. But often it is not the center that matters, it is the edges: how long the pizza takes if you're unlucky? How long do the slowest 5% of orders wait? What do the top 10% earn? These questions are answered by percentiles β one of an analyst's most practical tools. A percentile tells you what share of the data lies below a given value.
p90 = 40 min: 90% of the data lies below this value (shaded). On skewed data the tail percentiles (p90, p99) matter more than the mean β they say "how bad it gets for the unluckiest". That is how SLAs are set: "95% of requests faster than X".
Before you is the delivery time across all the chain's orders. A percentile is the value below which a given share of the data lies. Move the p slider: the shaded part of the histogram is the p% of values to the left, and the yellow line is the percentile value itself. p50 is the median: half the orders are faster. p90 is the threshold below which 90% of deliveries sit β above it, the slowest 10%.
Percentiles are the language of monitoring and SLAs. The requirement "95% of requests faster than 200 ms" is about p95, not the mean. Reliability teams watch the tail percentiles (p95, p99) precisely because the mean response time is deceptive β a few very slow requests inflate it, while many equally slow ones hide behind an acceptable average. A percentile shows what a specific share of users actually experiences.
In product analytics percentiles describe the user distribution: the median receipt, the top 10% by revenue (where the profit usually sits), the bottom 25% by activity (churn candidates).
Children's growth charts are percentile curves: a child at the 3rd percentile is small, at the 97th β large. The doctor reads the percentile, not the absolute number.
Salary surveys publish market p25/p50/p75: you see the range instead of a deceptive "industry average" inflated by the top earners.