Definition
Central tendency is the property of a data set captured by a single number that locates the middle of the distribution. The three classical measures are the arithmetic mean (the sum of values divided by their count), the median (the value that splits the ordered data in half), and the mode (the value or category that occurs most often). Each answers a different version of the question "what is typical here?" and each can be the right or wrong choice depending on the shape of the distribution.
In symmetric distributions without extreme values, the three measures agree closely. In skewed distributions — incomes, house prices, hospital stays — they diverge sharply, and the choice between them shapes the story the data tells. Reporting a mean income alongside a median exposes inequality that either number alone would obscure.
Why it matters
How it works
The arithmetic mean is computed by adding every value and dividing by the number of values. It uses every observation, which makes it efficient when the distribution is symmetric, but the same property makes it vulnerable: a single extreme outlier can drag the mean far from where most of the data sits. The median is computed by sorting the data and taking the middle value, or the average of the two middle values when the count is even. Because it depends only on the rank of each observation rather than its magnitude, the median is robust to outliers and extreme tails.
The mode is the most frequently occurring value or category. For continuous data it is usually defined as the peak of a histogram or density estimate rather than an exact value. A distribution may be unimodal, bimodal, or multimodal, and the number and location of modes can reveal that what looks like one population is actually a mixture of several. The right central-tendency measure depends on the question being asked, the type of data, and the shape of the distribution — choosing well is half of summarising data honestly.