Statistic

A statistic singular or sample statistic is any quantity computed from values in a sample which is considered for the statistical purpose. Statistical purposes add estimating a population parameter, describing a sample, or evaluating a hypothesis. The average or mean of pattern values is a statistic. The term statistic is used both for the function together with for the return of the function on a condition sample. When a statistic is being used for a particular purpose, it may be intended to by a score indicating its purpose.

When a statistic is used for estimating a population parameter, the statistic is called an estimator. A population argument is any characteristic of a population under study, but when it is for not feasible to directly degree the return of a population parameter, statistical methods are used to infer the likely value of the parameter on the basis of a statistic computed from a sample taken from the population. For example, the sample mean is an unbiased estimator of the population mean. This means that the expected value of the sample intend equals the true population mean.

A descriptive statistic is used to summarize the sample data. A test statistic is used in statistical hypothesis testing. Note that a single statistic can be used for institution purposes – for example the sample intend can be used to estimate the population mean, to describe a sample data set, or to test a hypothesis.

Properties

A statistic is an observable random variable, which differentiates it both from a parameter that is a generally unobservable quantity describing a property of a statistical population, and from an unobservable random variable, such(a) as the difference between an observed measurement and a population average. A parameter can only be computed exactly if the entire population can be observed without error; for instance, in a perfect census or for a population of standardized test takers.

Statisticians often contemplate a parameterized family of probability distributions, any ingredient of which could be the distribution of some measurable aspect of used to refer to every one of two or more people or matters member of a population, from which a sample is drawn randomly. For example, the parameter may be the average height of 25-year-old men in North America. The height of the members of a sample of 100 such(a) men are measured; the average of those 100 numbers is a statistic. The average of the heights of all members of the population is not a statistic unless that has somehow also been ascertained such(a) as by measuring every detail of the population. The average height that would be calculated using all of the individual heights of all 25-year-old North American men is a parameter, and not a statistic.

Important potential properties of statistics increase completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.

Information of a statistic on good example parameters can be defined in several ways. The near common is the Fisher information, which is defined on the statistic model induced by the statistic. Kullback information degree can also be used.