Table of Contents
Measures of Central Tendency
Mean, median, and mode are the three primary measures of central tendency in statistics. They each describe the center of a dataset in different ways. The mean is the arithmetic average, the median is the middle value when sorted, and the mode is the most frequently occurring value.
Choosing the right measure depends on your data. The mean is most common but sensitive to outliers. The median is more robust and better for skewed data. The mode is useful for categorical data or identifying the most common value.
Formulas
Comparison
| Property | Mean | Median | Mode |
|---|---|---|---|
| Affected by outliers | Yes | No | No |
| Works with categorical | No | No | Yes |
| Always unique | Yes | Yes* | No |
| Uses all data | Yes | No | No |
Frequently Asked Questions
When is the mean not a good measure?
The mean is not ideal for skewed distributions or data with extreme outliers. For example, in income data where a few very high earners raise the average, the median better represents the typical person's income.
What if there are multiple modes?
Data can be bimodal (two modes), multimodal (three or more modes), or have no mode if all values occur with equal frequency. This calculator reports all modes if multiple exist.
How are mean, median, and mode related in a normal distribution?
In a perfectly normal (bell-shaped) distribution, the mean, median, and mode are all equal. In a right-skewed distribution, mean > median > mode. In a left-skewed distribution, mean < median < mode.