Percentile

A percentile is the value below which a given percentage of observations in a dataset fall. The 90th percentile is the value beating 90% of the data; the median is the 50th percentile.

Percentiles are useful when the distribution isn’t normal — which is most of the time. Mean and standard deviation describe a normal distribution well; percentiles describe any distribution by reporting where its mass sits. Income distribution, latency measurements, and test scores are all commonly reported via percentiles for this reason.

Computing a percentile is straightforward in concept, fiddly in practice. The naive “the value at rank p × n in the sorted data” approach works when p × n is an integer; otherwise you have to interpolate. The most common method is linear interpolation between the two closest ranks, which is the default in NumPy (linear) and the NIST reference. R supports nine different percentile algorithms via the type parameter — they typically disagree by less than half a percentile point.

Quartiles are the 25th, 50th, and 75th percentiles (Q1, Q2 = median, Q3). The interquartile range (IQR) = Q3 − Q1 is a robust measure of spread — robust because it ignores the outer 25% of data on each end, where outliers do their damage.

Use our statistics calculator for any percentile against a pasted dataset.