Heuristic
Choose the average that fits the question
The arithmetic mean can be correct and still describe nobody's ordinary day.
When it fits
- A single 'average' seems unlike most observations.
When to avoid it
- A median does not make expensive or dangerous tail cases irrelevant.
Why it matters
Compare the mean with the median and inspect the distribution. The mean retains the influence of large magnitudes; the median identifies the ordered middle. Decide whether the question concerns totals and load, a typical case, or something else before selecting the summary.
An example
Durations of 1, 1, 1, 1 and 21 minutes have a mean of 5 and a median of 1. The long case still matters for total workload.
Check your result
The chosen summary serves the decision rather than merely sounding more favorable.
Keep this limit in mind
- A median does not make expensive or dangerous tail cases irrelevant.
Connected ideas
Useful withPut variation beside the average
Evidence and sources
Supports
The mean uses every magnitude, while the median is based on the ordered middle; extreme values can therefore affect them differently.
Neither measure is automatically the best summary for every decision.
NIST/SEMATECH e-Handbook, 1.3.5.1: Measures of Location · Definition of Location; effects of heavy tails