Order statistic

An order statistic is a value selected by rank after a sample is sorted. The minimum, maximum, and median are common examples.

Sample (statistics): A sample is a subset of observations collected from a population for statistical analysis. Order statistics are ranks within a sample, rather than within the full population.
Sorting algorithm: A sorting algorithm arranges data items in a specified order. Sorting makes the rank defining each order statistic explicit.
Sample quantile: A sample quantile is a cutoff estimated from an ordered sample at a specified cumulative proportion. It is computed from one or more sample order statistics, depending on the convention.
Arithmetic mean: The arithmetic mean is the sum of numerical values divided by their count. Unlike a ranked value, the mean combines every observation through its magnitude.
Quantile: A quantile is a value that divides an ordered distribution or dataset at a specified probability or proportion. Sample quantiles are often defined using one or more order statistics.
Joint distribution: A joint distribution describes the probabilities of possible values of two or more random variables together. Order statistics from the same sample are dependent, so their joint law matters.
Tolerance interval: A tolerance interval is an interval estimated to contain a specified proportion of a population with stated confidence. Its endpoints can be chosen from sample order statistics to avoid distributional assumptions.
Mode (statistics): The mode is the most frequent value in a dataset or the highest point of a probability distribution. A mode is selected by frequency or density, not by position in sorted data.
Median: The median is the central value of an ordered dataset, or the average of the two central values when its size is even. The median is a central order statistic, with conventions for even-sized samples.
Probability density function: A probability density function describes the relative likelihood of values for a continuous random variable. For continuous samples, densities of ranked values follow from the parent density and rank.

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