Why the choice matters
The mean and the median can tell different stories about the same data. For skewed measures such as costs, wait times or income, a few large values pull the mean up while the median barely moves. Choosing one without a reason can mislead readers, intentionally or not.
Three questions
1. What decision does the number serve? If the total matters (budgeting a program's cost, planning staffing hours), the mean is the right summary because mean × number of people equals the total. If the question is "what is typical for a person," the median is usually closer to what readers mean.
2. What does the distribution look like? Plot it first. A roughly symmetric distribution gives similar means and medians, and either works. A long right tail (a few very large values) separates them. Do not decide from a table of summaries alone.
3. What will readers assume? Many readers read "average" as "typical." If your mean is far above the median, a headline average will overstate the typical case. Say which one you are reporting and why.
When to report both
If the two differ noticeably, report both and say what the gap means: "Median wait was 12 days; the mean was 21 days because a few people waited more than 60 days." The gap itself is information about the tail.
A worked example (fictional)
Invented data. A program serves 10 families. Monthly assistance paid: nine families receive between $200 and $400, and one receives $4,000 because of an emergency.
- Median: about $300 — what a typical family received.
- Mean: about $670 — pulled up by the one large payment, but it is the number to use for budgeting, since 10 × $670 is the total paid.
A report that gave only the mean would suggest the typical family received more than twice as much as it did. A report that gave only the median would understate what the program cost. Giving both, plus the range, is the clear choice.
Other options
For heavy tails you can also report a trimmed mean or percentiles (25th, 75th), or analyze the log of the values and report ratios. Pick one because it answers your question, and say what you did.
Checklist
- Did I look at the distribution?
- Is the question about a total or about a typical case?
- Did I say which summary I used?
- Do the mean and median differ enough to report both?
Limits
This post is about describing data. Which summary to use in a statistical test is a separate question that depends on the test and the design.
Sources
General descriptive-statistics practice; add a textbook or reporting-guideline reference before approval.