Median and Mean
Also known as: average, typical value.
The mean is the sum divided by the count; the median is the middle value. Extreme values pull the mean but not the median.
Synthetic dataExamples on this page use synthetic data created for illustration.
Definition
The mean is the sum divided by the count; the median is the middle value when the data are sorted. The mean is pulled by extreme values, the median is not, so for skewed data such as prices or sales the two can tell very different stories.
In plain terms
“Average” usually means the mean, but it is one of several ways to say “typical”. With symmetric data the mean and median agree. With skewed data, where a few values are much larger than the rest, the mean is dragged toward the big ones while the median stays with the bulk. Incomes, sales per product and file sizes are all like this.
Neither is always right. The mean is what you need for totals (total sales = mean × count); the median describes the typical case. Say which you use.
Example
Monthly sales of seven products: 2, 3, 3, 4, 5, 6 and 300.
| Summary | Value | What it tells you |
|---|---|---|
| Mean | 46.1 | Total sales divided by products; no single product sells anywhere near this |
| Median | 4 | A typical product |
Reporting “the average product sells 46” would be accurate arithmetic and a misleading picture.
Common misunderstandings
- “Average always means the mean.” Check which measure is meant; many reports do not say.
- “The median is always the better choice.” For totals and budgets the mean is the quantity you need.
- “The average of percentages is the overall percentage.” Only if every group has the same size.
References
- David Spiegelhalter. The Art of Statistics: How to Learn from Data . Basic Books, 2019. ISBN 978-1541618510.
- NIST/SEMATECH e-Handbook of Statistical Methods . NIST.