Statistical population#Mean

{{Short description|Complete set of items that share at least one property in common}}

{{For|the number of people|Population}}

In statistics, a population is a set of similar items or events which is of interest for some question or experiment.{{Cite journal |last=Haberman |first=Shelby J. |date=1996 |title=Advanced Statistics |url=https://link.springer.com/book/10.1007/978-1-4757-4417-0 |journal=Springer Series in Statistics |language=en |doi=10.1007/978-1-4757-4417-0 |isbn=978-1-4419-2850-4 |issn=0172-7397}}{{Cite web|title=Glossary of statistical terms: Population|website=Statistics.com|url=http://www.statistics.com/glossary&term_id=812|access-date=22 February 2016}} A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypothetical and potentially infinite group of objects conceived as a generalization from experience (e.g. the set of all possible hands in a game of poker).{{MathWorld|Population}}

A population with finitely many values $N$ in the supportDrew, J. H., Evans, D. L., Glen, A. G., Leemis, L. M. (n.d.). Computational Probability: Algorithms and Applications in the Mathematical Sciences. Deutschland: Springer International Publishing. Page 141 https://www.google.de/books/edition/Computational_Probability/YFG7DQAAQBAJ?hl=de&gbpv=1&dq=%22population%22%20%22support%22%20of%20a%20random%20variable&pg=PA141 of the population distribution is a finite population with population size $N$. A population with infinitely many values in the support is called infinite population.

A common aim of statistical analysis is to produce information about some chosen population.{{cite book | last1 = Yates | first1 = Daniel S. | last2 = Moore | first2 = David S | last3 = Starnes | first3 = Daren S. | year = 2003 | title = The Practice of Statistics | edition = 2nd | publisher = Freeman | location = New York | url = http://bcs.whfreeman.com/yates2e/ | isbn = 978-0-7167-4773-4 | url-status = dead | archive-url = https://web.archive.org/web/20050209001108/HTTP://bcs.whfreeman.com/yates2e/ | archive-date = 2005-02-09 }}

In statistical inference, a subset of the population (a statistical sample) is chosen to represent the population in a statistical analysis.{{Cite web|title=Glossary of statistical terms: Sample|website=Statistics.com|url=http://www.statistics.com/glossary&term_id=281|access-date=22 February 2016}} Moreover, the statistical sample must be unbiased and accurately model the population. The ratio of the size of this statistical sample to the size of the population is called a sampling fraction. It is then possible to estimate the population parameters using the appropriate sample statistics.{{Cite book |last1=Levy |first1=Paul S. |url=https://books.google.com/books?id=XU9ZmLe5k1IC |title=Sampling of Populations: Methods and Applications |last2=Lemeshow |first2=Stanley |date=2013-06-07 |publisher=John Wiley & Sons |isbn=978-1-118-62731-0 |language=en}}

For finite populations, sampling from the population typically removes the sampled value from the population due to drawing samples without replacement. This introduces a violation of the typical independent and identically distribution assumption so that sampling from finite populations requires "finite population corrections" (which can be derived from the hypergeometric distribution). As a rough rule of thumb,Hahn, G. J., Meeker, W. Q. (2011). Statistical Intervals: A Guide for Practitioners. Deutschland: Wiley. Page 19. https://www.google.de/books/edition/Statistical_Intervals/ADGuRxqt5z4C?hl=de&gbpv=1&dq=infinite%20population&pg=PA19 if the sampling fraction is below 10% of the population size, then finite population corrections can approximately be neglected.