A table of the number of occurrences of each of a set of classified observations. The occurrences might arise from the throw of dice, the measurement of a man’s height in a particular range of values, or the number of reported cases of a disease in different groups of people classified by their age, sex, or other category.

It is usual practice to choose a fairly small number of categories so that the relative frequencies within categories are not too small. If no definite upper or lower limits are known, all values above (or below) a certain value are grouped into a single category known as the upper (or lower) tail.

Frequency distributions may be summarized by computing statistics such as the mean (or other measures of location) and the standard deviation (or other measures of variation), and sometimes measures of asymmetry or skewness and of compactness (i.e. the proportion of the sample in the centre and in the tails).

The term frequency distribution is applied to observed data in a sample. In contrast, probability distributions are theoretical formulas for the probability of observing each event. Fitting probability distributions to observed frequency distributions is a fundamental statistical method of data analysis.