# Sample (statistics)

In statistics and quantitative research methodology, a sample is a set of individuals or objects collected or selected from a statistical population by a defined procedure.[1] The elements of a sample are known as sample points, sampling units or observations.[citation needed] When conceived as a data set, a sample is often denoted by capital roman letters such ${\displaystyle X}$ and ${\displaystyle Y}$, with its elements expressed in lower-case (e.g., ${\displaystyle x_{3}}$) and the sample size denoted by the letter ${\displaystyle n}$.[2][3]

Typically, the population is very large, making a census or a complete enumeration of all the individuals in the population either impractical or impossible. The sample usually represents a subset of manageable size. Samples are collected and statistics are calculated from the samples, so that one can make inferences or extrapolations from the sample to the population.

The sample may be drawn from a population 'without replacement' (i.e. no element can be selected more than once in the same sample), in which case it is a subset of a population; or 'with replacement' (i.e. an element may appear multiple times in the one sample), in which case it is a multisubset.[4]