In statistics, a population is a set of similar items which is of interest for some question or experiment.1 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).2
In statistical inference, the population is modelled by a probability distribution with unknown parameters.3 By analyzing a subset of the population, it is then possible to estimate the population parameters using the appropriate sample statistics.4
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.5 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.6
See also
See also
References
References
- Haberman, Shelby J. (1996). "Advanced Statistics". Springer Series in Statistics: 1. doi:10.1007/978-1-4757-4417-0. ISBN 978-1-4419-2850-4. ISSN 0172-7397.
- Weisstein, Eric W. "Statistical population". MathWorld.
- Yates, Daniel S.; Moore, David S.; Starnes, Daren S. (2003). The Practice of Statistics (2nd ed.). New York: Freeman. ISBN 978-0-7167-4773-4. Archived from the original on 2005-02-09.
- Levy, Paul S.; Lemeshow, Stanley (2013-06-07). Sampling of Populations: Methods and Applications. John Wiley & Sons. ISBN 978-1-118-62731-0.
- Yates, Daniel S.; Moore, David S.; Starnes, Daren S. (2003). The Practice of Statistics (2nd ed.). New York: Freeman. ISBN 978-0-7167-4773-4. Archived from the original on 2005-02-09.
- Schaum's Outline of Theory and Problems of Probability by Seymour Lipschutz and Marc Lipson, p. 141