Statistic

A statistic is a numerical summary of observed values for a random variable (or variables) in a sample. The term random indicates that the variable's value, and thus its statistic, may differ across samples that are drawn from the same sample population. A statistic is used to estimate a parameter, a numerical summary of a given variable (or variables) in the population.

A statistic is commonly represented with the common alphabet rather than with Greek letters, as is typically the case with a parameter. For example, a statistic such as a standard deviation is represented by s, whereas the corresponding population parameter is represented by σ.

Describing characteristics of a sample variable (or variables) is often called descriptive statistics. Examples include computing the sample's mean or standard deviation on a variable such as age or weight or describing proportions for categorical variables such as race or marital status. The process of using the sample's descriptive data to generate population estimates is typically referred to as inferential statistics.

It should be recognized that if data are available for the entire population of interest, inference is unnecessary as the parameter can be calculated directly.