Percentile
Also known as: quantile, quartile.
The value below which a given percentage of observations fall. The 50th percentile is the median; the 90th marks the value that 90% do not exceed.
Synthetic dataExamples on this page use synthetic data created for illustration.
Definition
The p-th percentile is the value below which p percent of the observations fall. The 50th percentile is the median; the 90th marks the value that 90% of observations do not exceed. Percentiles describe position within a distribution and are not thrown off by extreme values.
In plain terms
Percentiles are what you want when the question is “how bad is the bad case?” rather than “what is the average?”: delivery time for nine in ten orders, price in the top tenth of a category. Quartiles are the 25th, 50th and 75th percentiles.
Software computes percentiles in several slightly different ways, which matters for small samples. A reported percentile should say how many observations it rests on, and ideally which method produced it.
Example
Ten delivery times in days, sorted: 1, 2, 2, 3, 3, 4, 4, 5, 8, 20.
| Quantity | Value |
|---|---|
| Median (50th percentile) | 3.5 days |
| Mean | 5.2 days |
| 90th percentile, “nearest rank” method (the 9th value) | 8 days |
| 90th percentile, linear interpolation | 9.2 days |
Nine in ten orders arrive within about 8 to 9 days; the one 20-day order drags the mean above the median. The two methods disagree because ten observations are too few to pin the 90th percentile down.
Common misunderstandings
- “A percentile is a percentage score.” It is a position in a distribution, not a share of correct answers.
- “All tools give the same percentile.” Definitions differ, visibly so for small samples.
- “The 90th percentile is the average of the top 10%.” It is the cut-off value, not the mean above it.
References
- Rob J. Hyndman, Yanan Fan. Sample Quantiles in Statistical Packages . The American Statistician, 1996. DOI: 10.1080/00031305.1996.10473566
- NIST/SEMATECH e-Handbook of Statistical Methods . NIST.