Learn the formulas for mean, median, and mode with worked examples, and discover when to use each measure of central tendency.
Central tendency is a statistical concept that identifies a single value representing the "center" or "typical value" of a dataset. The three most common measures of central tendency are the mean, median, and mode. Each measure answers the same question differently: "What is a typical value in this data?" Choosing the right one depends on the shape of your data and the question you are trying to answer.
where n = number of values in the dataset
where f is the frequency (count) of each value in the dataset
| Feature | Mean | Median | Mode |
|---|---|---|---|
| Definition | Sum divided by count | Middle value when sorted | Most frequent value |
| Affected by outliers | Yes, heavily | No | No |
| Best for | Symmetric data | Skewed data | Categorical data |
| Always unique? | Yes | Yes | No, can have 0, 1, or many |
| Works with non-numeric data? | No | No | Yes |
| Easy to calculate? | Yes, simple arithmetic | Requires sorting first | Requires counting frequencies |
| Common real-world use | Average salary, GPA | Median home price | Most popular product |
Use Mean -> Symmetric data, no outliers (e.g., test scores, average revenue)
Use Median -> Skewed data or outliers present (e.g., home prices, income)
Use Mode -> Categorical data or finding most common (e.g., popular product)In everyday language, "average" and "mean" are used interchangeably. Technically, "average" can refer to any measure of central tendency (mean, median, or mode), but the arithmetic mean is the most common type. When someone says "average," they almost always mean the arithmetic mean.
Yes. If every value in a dataset appears exactly once (for example, 3, 7, 12, 18), then no value repeats and the dataset has no mode.
Income data is typically right-skewed because a small number of very high earners pull the mean upward. For instance, if 9 people earn $50,000 and 1 person earns $5,000,000, the mean is $545,000 but the median is $50,000. The median more accurately represents the typical earner.
Sort the numbers in ascending order, then take the two middle values and calculate their average. For example, in the sorted set 2, 4, 6, 8, the two middle values are 4 and 6 so the median is (4 + 6) / 2 = 5.
A bimodal dataset has two values that appear with equal highest frequency. For example, in the set 1, 2, 2, 5, 5, 7, both 2 and 5 appear twice. Bimodal distributions often indicate that the data comes from two distinct groups mixed together.
Yes, and they often are. In a perfectly symmetric distribution (like a bell curve), all three are equal. In a skewed distribution, they diverge. For example, in the set 1, 2, 2, 3, 10, the mode is 2, the median is 2, and the mean is 3.6.
