Statistical population

Source: Wikipedia, the free encyclopedia.
For the number of people, see Population.

In

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).[3]
A population with finitely many values in the support[4] of the population distribution is a finite population with population size . 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.[5] In

sample statistics.[7]

For finite populations, sampling from the population typically removes the sampled value from the population

finite population corrections" (which can be derived from the hypergeometric distribution). As a rough rule of thumb[8]
, if the sampling fraction is below 10% of the population size, then finite population corrections can approximately be neglected.

Mean

The population mean, or population

discrete probability distribution
of a random variable , the mean is equal to the sum over every possible value weighted by the probability of that value; that is, it is computed by taking the product of each possible value of and its probability , and then adding all these products together, giving .
continuous probability distribution. Not every probability distribution has a defined mean (see the Cauchy distribution
for an example). Moreover, the mean can be infinite for some distributions.

For a finite population, the population mean of a property is equal to the arithmetic mean of the given property, while considering every member of the population. For example, the population mean height is equal to the sum of the heights of every individual—divided by the total number of individuals. 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.[12]

See also

References

  1. ISSN 0172-7397
    .
  2. ^ "Glossary of statistical terms: Population". Statistics.com. Retrieved 22 February 2016.
  3. ^ Weisstein, Eric W. "Statistical population". MathWorld.
  4. ^ Drew, 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
  5. ISBN 978-0-7167-4773-4. Archived from the original
    on 2005-02-09.
  6. ^ "Glossary of statistical terms: Sample". Statistics.com. Retrieved 22 February 2016.
  7. ISBN 978-1-118-62731-0
    .
  8. ^ 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
  9. ISBN 0471257087. {{cite book}}: ISBN / Date incompatibility (help
    )
  10. ^ Elementary Statistics by Robert R. Johnson and Patricia J. Kuby, p. 279
  11. ^ Weisstein, Eric W. "Population Mean". mathworld.wolfram.com. Retrieved 2020-08-21.
  12. ^ Schaum's Outline of Theory and Problems of Probability by Seymour Lipschutz and Marc Lipson, p. 141
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