Editing Mathematical statistics (section)

===Statistical inference===
{{main|Statistical inference}}
[[Statistical inference]] is the process of drawing conclusions from data that are subject to random variation, for example, observational errors or sampling variation.<ref name="Oxford">Upton, G., Cook, I. (2008) ''Oxford Dictionary of Statistics'', OUP. {{isbn|978-0-19-954145-4}}</ref> Initial requirements of such a system of procedures for [[inference]] and [[Inductive reasoning|induction]] are that the system should produce reasonable answers when applied to well-defined situations and that it should be general enough to be applied across a range of situations. Inferential statistics are used to test hypotheses and make estimations using sample data. Whereas [[descriptive statistics]] describe a sample, inferential statistics infer predictions about a larger population that the sample represents.

The outcome of statistical inference may be an answer to the question "what should be done next?", where this might be a decision about making further experiments or surveys, or about drawing a conclusion before implementing some organizational or governmental policy.
For the most part, statistical inference makes propositions about populations, using data drawn from the population of interest via some form of random sampling. More generally, data about a random process is obtained from its observed behavior during a finite period of time. Given a parameter or hypothesis about which one wishes to make inference, statistical inference most often uses:
* a [[statistical model]] of the random process that is supposed to generate the data, which is known when randomization has been used, and
* a particular realization of the random process; i.e., a set of data.