Direct comparison
Mean vs Median: Which Measure of Average to Use | CASRAI
Mean vs median explained: the mean divides the total equally and is sensitive to outliers; the median is the middle value and is robust to skewed distributions.
Side-by-side comparison
| Dimension | Mean | Median |
|---|---|---|
| Definition | Sum of all values divided by the count. | The middle value when data are sorted in order. |
| Sensitivity to outliers | High — one extreme value shifts the mean markedly. | Low — extreme values do not affect the middle position. |
| Best for | Symmetric, normally distributed data without extreme outliers. | Skewed distributions and data with outliers. |
| Typical uses | Test scores (if normally distributed), temperature, height. | Income, house prices, waiting times, ordinal survey data. |
| Effect of skew | Pulled in the direction of the tail. | Stays near the centre of the bulk of data. |
| Use of all data | Yes — every value contributes. | No — depends only on rank position. |
| Mathematical use | Preferred for further statistical analysis (e.g. t-tests). | Less amenable to algebra but more robust descriptively. |
| Relationship in skewed data | Right-skewed: mean > median; left-skewed: mean < median. | Sits between mean and mode in a skewed distribution. |
Common questions
FAQ
Why do income statistics usually report the median rather than the mean?+
Because income distributions are strongly right-skewed: a small number of very high earners pull the mean well above the income of a typical household. The median — the income of the person exactly in the middle of the distribution — gives a more representative picture of what most people earn.
When is the mean a better choice than the median?+
When the data are roughly symmetrically distributed and do not contain extreme outliers, the mean is preferred. It uses all the information in the dataset and is required for most parametric statistical tests such as t-tests and ANOVA, which are built on mean-based assumptions.
What happens to the mean and median in a perfectly symmetrical distribution?+
They are equal. In a perfectly symmetrical distribution (such as the normal distribution), the mean, median, and mode all coincide at the centre. Divergence between the mean and median is itself a useful signal of skewness in the data.
Going deeper
