# Dictionary Definition

statistic n : a datum that can be represented
numerically

# User Contributed Dictionary

## English

### Etymology

From statistik, from statisticum ("of the state") and statista ("statesman" or "politician"); Statistik, first introduced by Gottfried Achenwall (1749), originally designated the analysis of data about the state.### Adjective

- Alternative spelling of statistical.

#### Translations

See: statistical### Noun

- A single item in a statistical study.
- A quantity calculated from the data in a sample, which characterises an important aspect in the sample (such as mean or standard deviation).
- A person, or personal event, reduced to being an item of
statistical information.
- By dying from an overdose, he became just another statistic.

#### Derived terms

#### Translations

single item of a statistical study

- Finnish: tilastotieto

quantity calculated from the data in a sample

- Finnish: tunnusluku, tilastotieto

something reduced to an item in a statistic

- Finnish: tilastotieto

# Extensive Definition

A statistic (singular) is the result of applying
a function
(statistical algorithm) to a set of
data.

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.

A statistic is distinct from an unknown statistical
parameter, which is not computable from a sample. A key use of
statistics is as estimators in statistical
inference, to estimate parameters of a distribution given a
sample. For instance, the sample mean is a statistic, while the
population mean is a parameter.

## 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. Thus the arithmetic mean is a
statistic, which is frequently used as an estimator for the
generally unobservable population
mean parameter.

Other examples of statistics include

- Sample mean and sample median
- Sample variance and sample standard deviation
- Sample quantiles besides the median, e.g., quartiles and percentiles
- t statistics, chi-square statistics, f statistics
- Order statistics, including sample maximum and minimum
- Sample moments and functions thereof, including kurtosis and skewness
- Various functionals of the empirical distribution function

## Properties

### Observability

A statistic is an observable random
variable, which differentiates it from a parameter,
a generally unobservable quantity describing a property of a
statistical
population.

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. 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.

## Footnotes

statistic in German: Statistik

statistic in Spanish: Estadístico

statistic in French: Statistiques

statistic in Italian: Statistica

statistic in Dutch: Steekproeffunctie

statistic in Japanese: 統計量

statistic in Finnish: Tunnusluku

statistic in Thai: ค่าสถิติ

statistic in Portuguese: Estatística
(função)