What is Sampling (statistics)?
[[File:Bundesarchiv Bild 183-1989-1128-012, Berlin, Rauschgiftspürhund im Einsatz.jpg|thumb|Border police looking for [[illegal drugs]] with a specially trained dog: If they check every tenth car, they are taking an unbiased sample.]] {{about|||Sampling}} In [[statistics]], a '''sample''' is part of a [[population (statistics)|population]]. The sample is carefully chosen. It should represent the whole population fairly, without [[bias]]. When treated as a data set, a sample is often represented by [[Capital letter|capital letters]] such as <math>X</math> and <math>Y</math>, with its elements being represented in lowercase (e.g., <math>x_3</math>), and the [[sample size]] being represented by the letter <math>n</math>.<ref>{{Cite web|date=2020-04-26|title=List of Probability and Statistics Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/probability-statistics-symbols/|access-date=2020-08-21|website=Math Vault|language=en-US}}</ref> The reason samples are needed is that populations may be so large that counting all the individuals may not be possible or practical. Therefore, solving a problem in statistics usually starts with '''sampling'''.<ref>Lohr, Sharon L. 1999. ''Sampling: design and analysis''. Duxbury.</ref> Sampling is about choosing which [[Information|data]] to take for later [[analysis]]. As an example, suppose the [[pollution]] of a [[lake]] should be analysed for a study. Depending on where the samples of [[water]] were taken, the studies can have different results. As a general rule, samples need to be [[random]]. This means the chance or [[probability]] of selecting one individual is the same as the chance of selecting any other individual. In practice, [[Random sample|random samples]] are always taken by means of a well-defined [[wikt:procedure|procedure]]. A procedure is a set of [[rule]]s, a sequence of steps written down and exactly followed. Even so, some bias may remain in the sample. Consider the problem of designing a sample to predict the result of an [[election]] [[wikt