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Submitted by on Apr 29, 2021

In statistics and quantitative research methodology, a sample is a collection of individuals or objects collected or selected by a statistical population using a specific procedure. The elements of a sample are known as sample points, units of measure, or observations. When intended as a dataset, the sample is often denoted in uppercase Latin letters such as {\ display style X} X and {\ display style Y} Y, with lowercase elements (for example, {\ display style x_ {3} } x_ {3}) and the sample size denoted by the letter {\ displaystyle n}.

The population is usually very large, making it impractical or impossible to conduct a census or complete registration of all individuals in the population. The sample is typically a subset of the manageable size. Samples are collected, and statistics are calculated from them so that conclusions can be drawn or data from the sample can be extrapolated to the population.

The sample can be taken from the general population without replacement (i.e., no item can be selected more than once in the same sample), in which case it is a subset of the general population; or by substitution (i.e. an element can appear several times in one sample), in this case, it is a multisubset.

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A complete sample is a set of items from a parent population that includes all items that meet a set of well-defined selection criteria. For example, a complete sample of Australian men taller than 2m would include a list of every Australian man taller than 2m. But this would not include German males, tall Australians females or people under 2m. Thus, such a complete sample requires a complete listing of the parent population, including height, sex, and nationality data for each member of that parent population. In the case of human populations, such a complete list is unlikely (the human population is in the billions) to exist. But such complete samples are often available in other disciplines, such as recruiting players in a major sports league, birth dates of MPs, or a complete list of astronomical objects of limited size.

An unbiased (representative) sample is a collection of features selected from a full sample using a selection process that is independent of feature properties. For example, an unbiased sample of Australian men taller than 2m might be a random subset of 1% of Australian men taller than 2m. But one chosen from the electoral register might not be unbiased since, For example, men under 18 will not be on the voter lists. In an astronomical context, an objective sample may consist of that portion of the full sample for which data are available, provided that the availability of the data is independent of the individual properties of the source.

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