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For other uses, see Statistics (disambiguation).

A statistic (singular) is the result of applying a function (statistical algorithm) to a set of data. The Mathematical concept of a function expresses dependence between two quantities one of which is given (the independent variable, argument of the function In Mathematics, Computing, Linguistics and related subjects an algorithm is a sequence of finite instructions often used for Calculation A data set (or dataset) is a collection of Data, usually presented in tabular form

More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution: the term is used both for the function and for the value of the function on a given sample. In Statistics, a sample is a Subset of a population. Typically the population is very large making a Census or a complete Enumeration

A statistic is distinct from an unknown statistical parameter, which is not computable from a sample. A statistical parameter is a parameter that indexes a family of Probability distributions Among parameterized families of distributions are the Normal distributions A key use of statistics is as estimators in statistical inference, to estimate parameters of a distribution given a sample. In Statistics, an estimator is a function of the observable sample data that is used to estimate an unknown population Parameter (which is called the Inferential statistics or statistical induction comprises the use of Statistics to make Inferences concerning some unknown aspect of a Population For instance, the sample mean is a statistic, while the population mean is a parameter.

Contents

Examples

In the calculation of the arithmetic mean, for example, the algorithm consists of summing all the data values and dividing this sum by the number of data items. In Mathematics and Statistics, the arithmetic Mean (or simply the mean) of a list of numbers is the sum of all the members of the list divided Debt AIDS Trade in Africa (or DATA) is a Multinational non-government organization founded in January 2002 in London by U2 's Thus the arithmetic mean is a statistic, which is frequently used as an estimator for the generally unobservable population mean parameter. In Statistics, mean has two related meanings the Arithmetic mean (and is distinguished from the Geometric mean or Harmonic mean

Other examples of statistics include

Properties

Observability

A statistic is an observable random variable, which differentiates it from a parameter, a generally unobservable quantity[1] describing a property of a statistical population. In Descriptive statistics, a quartile is any of the three values which divide the sorted Data set into four equal parts so that each part represents one fourth of A percentile is the value of a variable below which a certain percent of observations fall In Probability and Statistics, Student's t -distribution (or simply the t -distribution) is a Probability distribution Pearson's chi-square (&chi2 test is the best-known of several Chi-square tests – statistical procedures whose results are evaluated by reference An F-test is any Statistical test in which the test statistic has an F-distribution if the Null hypothesis is true In Statistics, the k th order statistic of a Statistical sample is equal to its k th-smallest value In Probability theory and Statistics, kurtosis (from the Greek word κυρτός kyrtos or kurtos, meaning bulging is a measure of the "peakedness" In Probability theory and Statistics, skewness is a measure of the asymmetry of the Probability distribution of a real -valued In Mathematics, a functional is traditionally a map from a Vector space to the field underlying the vector space which is usually the Real In Statistics, an empirical distribution function is a cumulative probability distribution function that concentrates probability 1/ n at each of the A random variable is a rigorously defined mathematical entity used mainly to describe Chance and Probability in a mathematical way A statistical parameter is a parameter that indexes a family of Probability distributions Among parameterized families of distributions are the Normal distributions In Statistics, a statistical population is a set of entities concerning which Statistical inferences are to be drawn often based on a Random sample

Statisticians often contemplate a parameterized family of probability distributions, any member of which could be the distribution of some measurable aspect of each member of a population, from which a sample is drawn randomly. In Probability theory and Statistics, a probability distribution identifies either the probability of each value of an unidentified Random variable 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 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 as by measuring every member of the population). The average height of all (in the sense of genetically possible) 25-year-old North American men is a parameter and not a statistic.

Statistical properties

Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience. In Statistics, completeness is a property of a Statistic for which the statistic optimally obtains information about the unknown parameters characterizing the distribution In Statistics, a consistent sequence of estimators is one which converges in probability to the true value of the parameter In Statistics, sufficiency is the property possessed by a Statistic, with respect to a Parameter, "when no other statistic which can be calculated In Statistics, the difference between an Estimator 's Expected value and the true value of the parameter being estimated is called the bias. In Statistics and Signal processing, a minimum mean square error ( MMSE) estimator describes the approach which minimizes the Mean square error In Probability theory and Statistics, the variance of a Random variable, Probability distribution, or sample is one measure of Robust statistics provides an alternative approach to classical statistical methods

Footnotes

  1. ^ A parameter can only be computed if the entire population can be observed without error, for instance in a perfect census or on a population of standardized test takers. A standardized test is a test administered and scored in a consistent manner

See also

Statistics is a mathematical science pertaining to the collection analysis interpretation or explanation and presentation of Data. The theory of statistics includes a number of topics Statistical models of the sources of data and typical problem formulation Sampling from a finite Descriptive Statistics are used to describe the basic features of the Data gathered from an experimental study in various ways A statistical hypothesis test is a method of making statistical decisions using experimental data

Dictionary

statistic

-adjective

  1. Alternative spelling of statistical.

-noun

  1. A single item in a statistical study.
  2. A quantity calculated from the data in a sample, which characterises an important aspect in the sample (such as mean or standard deviation).
  3. A person, or personal event, reduced to being an item of statistical information.
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