GlossaryStatistics and interpretation
Outlier
An outlier is an unusually distant observation. Learn why it requires investigation and why deleting it without a documented reason can mislead.
An outlier is an observation that is unusually distant from other observations in a dataset. It may reflect a recording error, an exceptional real event, or a limitation of the comparison being made. Identifying a value as unusual is a reason to investigate it, not automatic permission to remove it.
Unusual does not mean incorrect
NIST distinguishes erroneous observations from unusual values that may be valid or scientifically informative. Its guidance recommends investigation and methods that can accommodate extreme observations rather than simply deleting them without a basis. NIST detection of outliers.
In public-safety data, a very long interval could reflect a timestamp error, a delayed status entry, a different service category, or a genuinely prolonged response. The number alone cannot establish which explanation applies.
Example
Hypothetical example: Most eligible dispatch-to-arrival intervals in a file are between four and twelve minutes, but one is 180 minutes. An analyst checks the underlying timestamps and source notes.
If the arrival time was entered on the wrong date, a documented correction may be appropriate. If the record instead describes a valid exceptional delay, deleting it would remove part of the service experience. If it concerns a scheduled transfer outside the intended emergency-response scope, exclusion may follow the original eligibility rule rather than a desire to improve the average.
Common confusion
An outlier is not the same as the largest observation. Every finite dataset has a maximum, even when no value is unusually separated from the others. Nor does a fixed numerical cutoff suit every distribution or measure.
A formal outlier test depends on assumptions. A skewed distribution of service durations may naturally have a long upper tail. Applying a rule designed for another kind of distribution can flag valid observations as if they were errors.
Document the treatment
Record the basis for corrections or exclusions and retain the original information when appropriate for verification. A useful method note states whether implausible timestamps, duplicate records, or specific service types were removed and why.
If the value remains valid, show its effect on the summary. Comparing the mean with the median or reporting a wider distribution can help readers see how extreme observations influence the result. Removing inconvenient values without a disclosed rule can make performance appear more consistent than the underlying records support. The goal is an accurate account of the included activity, including exceptional cases.