The concept
The arithmetic mean adds values and divides by their count. The median is the middle value after sorting, or the average of the two middle values for an even count. They need not agree. Choose the summary that answers the question, and examine the distribution rather than treating one average as a complete description.
Worked example
A fictional repair desk records five waiting times: 2, 3, 3, 4, and 28 minutes. The mean is 40 divided by 5, or 8 minutes; the median is 3 minutes. The mean matters for total waiting burden, while the median better describes the middle visitor. Reporting only the median hides the visitor who waited 28 minutes. Reporting only the mean suggests a routine wait that none of the five visitors actually experienced.
Limits and judgment
An extreme value is not automatically an error. The long wait may reveal a genuine service problem. Provide the sample size, time period, and a measure of spread alongside the center. A useful public explanation might say that most observed waits were short but one unusually long case raised the mean substantially.
FROM UNDERSTANDING TO ACTION
Put it to work.
Calculate the mean and median of 4, 4, 5, 7, and 30; explain which question each answers.
RETRIEVE. REASON. REMEMBER.
Knowledge check.
Choose one answer for each question, then check your reasoning.
Sources & further reading.
Links support the core concepts or identify the book. Examples, exercises, and critical analysis are original Institute material. Source checks are not an independent expert review of every claim.
- NIST: Measures of Location ↗
Statistical core concept; all numerical scenarios and interpretations are original instructional examples. Source reviewed 2026-10-19.