Treat an outlier flag as a question
An outlier is a value that looks unusual relative to other observations. Its appearance depends on the data, the comparison group and the method used to flag it. A point beyond a box plot's usual range is a prompt to investigate; the plot cannot tell you whether the underlying record is wrong.
NIST's statistics handbook advises examining unusual observations because they can reveal information about the process or the way data were recorded. Before removing a value, ask what produced it. A long delivery time, for example, could be a typing error, a genuine delay or a different type of delivery that needs to be understood separately.
Check the record before choosing a remedy
Compare the value with the source record where access is appropriate. Check units, decimal points, category codes and any data conversion. A duration entered in hours among values recorded in minutes is a different problem from an unusually slow but correctly recorded task. Record the evidence behind any correction.
NIST distinguishes confirmed errors from observations whose origin remains uncertain. Correct a confirmed error when a reliable replacement exists. If the measurement is unusable, document how it is excluded from the relevant analysis. When no error is established, do not assume that distance from the average makes the observation disposable. Keep the original record and the decision history.
Understand what removal changes
Consider an invented set of delivery times: 2, 3, 3, 4 and 18 days. The mean is 6 days and the median is 3 days. Removing the 18-day delivery changes the mean to 3 days. If that delivery really occurred within the service being assessed, its removal hides an experience that may matter to the decision.
The mean and median answer different questions about a distribution. As NIST explains, extreme values affect the mean more strongly than the median. Reporting a median can help describe a typical observation, while reporting the range or longer delays preserves information about variability. The appropriate summary depends on what readers need to understand.
Consider the method and the context
Some outlier tests assume an approximately normal distribution. Applying them to strongly skewed data can flag values because the assumed distribution is unsuitable. NIST also cautions that tests designed for one outlier should not simply be repeated to identify several. A sequence of automatic deletions can become difficult to justify.
Review the data's shape and meaningful groups with the analyst. Depending on the question, an approach less sensitive to extreme observations may be appropriate. For the delivery example, separating service types would only make sense if those types were actually recorded and relevant. Do not invent groups after seeing the result simply to make an awkward value disappear.
Report the decision and its consequences
Write down which observations were flagged, the checks performed, the treatment chosen and the reason. Where there are defensible alternative treatments, consider showing whether the main conclusion changes across them. In the delivery example, the difference between the two averages is already a reason to explain the disputed observation.
If your conclusion depends heavily on a small number of records, make that dependence visible. For academic work, explain exclusions and analytical choices in the methods or supporting material, following your institution's requirements. The aim is an analysis whose decisions another reader can inspect, including decisions to retain unusual but credible data.