| Calculation | Sum of values / number of values |
|---|---|
| Unit | Same as the data |
| Sensitivity | Extreme values can shift it |
Definition and context
The arithmetic mean uses all the values in a set. It is calculated by adding them and dividing by the number of observations. It retains the unit of the data and is sensitive to changes in extreme values.
Consider a hypothetical set: 2, 4, and 12 minutes. The mean is 6 minutes, even though none of the observations has that value. This is not an error: the mean describes how the total is distributed, not necessarily an individual experience. To interpret it, it is helpful to know the median, dispersion, and how the data were selected. If we combine groups of different sizes, averaging their means without weighting may answer a different question from the mean of all the observations.
What we know and its limits
Introductory reference sheet. Properties and applications depend on measurement conditions; consult the sources before making comparisons.
Follow the evidence
The original sources for exploring this explanation and its limits.
- Introductory Statistics 2e · Measures of the Center
OpenStax · Rice University
Definitions of mean and median. - Engineering Statistics Handbook · Measures of Location
NIST / SEMATECH
Choosing measures of location according to the distribution.
Image credits
SciClue · AI-generated illustration (OpenAI) · Original source · Recurso editorial de SciClue · generado con IA