GlossaryStatistics and interpretation
Percentile
A percentile describes a position in ordered data. Learn why calculation methods, ties, sample size, and eligibility matter for response intervals.
A percentile is a value describing a position within an ordered distribution. A 90th-percentile interval summarizes the upper part of the included durations: roughly 90% are at or below that value under the chosen method. Exact results depend on the calculation convention, ties, and number of observations.
A value at a position
Percentiles help describe parts of a distribution that a mean or median does not show. A median is the 50th percentile. A higher percentile can help show the slower end of response intervals, although it still does not describe the single longest response.
NIST notes that percentile calculations can require interpolation between ordered observations and that there is no universally accepted interpolation method. Different software settings can therefore produce different answers from the same small set. NIST percentile guidance.
Example
Hypothetical example: A report lists ten ordered intervals of 2, 3, 4, 5, 6, 7, 8, 9, 10, and 20 minutes. It explicitly uses the nearest-rank method, selecting the observation at the rounded-up position given by percentile proportion multiplied by count.
For the 90th percentile, 0.90 × 10 gives position nine, or 10 minutes. Another method might interpolate differently. The result should be read with its stated method rather than treated as a software-independent constant.
Common confusion
The 90th percentile is not 90% of the longest value, nor the average of the slowest 10% of responses. In the example, 90% of the maximum would be 18 minutes, which is a different calculation.
A percentile is also distinct from a performance objective. A measured 90th-percentile interval of 10 minutes does not itself establish that 10 minutes is the appropriate target or that every call met it. Target definitions require their own authority and scope.
Reading operational percentiles
Identify the interval's start and end, included calls, period, and calculation method. A unit-level travel-time percentile and an incident-level first-arrival percentile summarize different observations.
Small groups can produce unstable percentile estimates, especially near the extremes. Rounding can make distinct results appear equal, and ties can put more than the stated percentage at or below the reported value. Comparing the sample count and a fuller distribution helps reveal those limits. Preserve missing or invalid durations as such; inserting zero values can alter the ordered positions and distort the result.