Statistical population

{{Short description|Complete set of items that share at least one property in common}} {{Other uses of|Population}} In statistics, a '''population''' is a set of similar items which is of interest for some question or experiment.<ref>{{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|url-access=subscription |pages=1}}</ref> 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).<ref>{{MathWorld|Population}}</ref>

In statistical inference, the population is modelled by a probability distribution with unknown parameters.<ref>{{cite book | last1 = Yates | first1 = Daniel S. | last2 = Moore | first2 = David S. |author-link2=David S. Moore| 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 }}</ref> By analyzing a subset of the population, it is then possible to estimate the population parameters using the appropriate sample statistics.<ref>{{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}}</ref>

==Mean== The '''population mean''' is the arithmetic mean of some numerical property across the entire population. Where the property under consideration is modelled by a random variable, the population mean refers to the expected value of that random variable.<ref>{{cite book |title=The Practice of Statistics|year=2003|publisher=Freeman|isbn=978-0-7167-4773-4|last1=Yates|first1=Daniel S.|last2=Moore|first2=David S.|author-link2=David S. Moore|last3=Starnes|first3=Daren S.|edition=2nd|location=New York|url=http://bcs.whfreeman.com/yates2e/|url-status=dead|archive-url=https://web.archive.org/web/20050209001108/HTTP://bcs.whfreeman.com/yates2e/|archive-date=2005-02-09}}</ref> Not every probability distribution has a well-defined mean (see the Cauchy distribution for an example).

The sample mean may differ from the population mean, especially for small samples. The law of large numbers states that the larger the size of the sample, the more likely it is that the sample mean will be close to the population mean.<ref>Schaum's Outline of Theory and Problems of Probability by Seymour Lipschutz and Marc Lipson, [https://books.google.com/books?id=ZKdqlw2ZnAMC&pg=PA141 p. 141]</ref>

==References== {{Reflist}}

==External links== *[http://www.socialresearchmethods.net/kb/sampstat.htm Statistical Terms Made Simple]

Category:Statistical theory