# Statistic

sample statisticempiricalmeasurestat
A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g. its arithmetic mean value).wikipedia
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### Sample mean and covariance

sample meansample covariancesample covariance matrix
For instance, the sample mean is a statistic that estimates the population mean, which is a parameter. Sample mean discussed in the example above and sample median
The sample mean or empirical mean and the sample covariance are statistics computed from a collection (the sample) of data on one or more random variables.

### Sample (statistics)

samplesamplesstatistical sample
A statistic (singular) or sample statistic is a single measure of some attribute of a sample (e.g. its arithmetic mean value). It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.
Samples are collected and statistics are calculated from the samples, so that one can make inferences or extrapolations from the sample to the population.

### Estimator

estimatorsestimateestimates
However, a statistic, when used to estimate a population parameter, is called an estimator.
An "estimator" or "point estimate" is a statistic (that is, a function of the data) that is used to infer the value of an unknown parameter in a statistical model.

### Test statistic

t-test of
When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.
A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing.

### Standard deviation

standard deviationssample standard deviationsigma
Sample variance and sample standard deviation
In cases where that cannot be done, the standard deviation σ is estimated by examining a random sample taken from the population and computing a statistic of the sample, which is used as an estimate of the population standard deviation.

### Statistical parameter

parametersparameterparametrization
However, a statistic, when used to estimate a population parameter, is called an estimator. A statistic is distinct from a statistical parameter, which is not computable in cases where the population is infinite, and therefore impossible to examine and measure all its items.
A parameter is to a population as a statistic is to a sample.

### Completeness (statistics)

completecompletenessboundedly complete
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 in relation to a model for a set of observed data.

### Sufficient statistic

sufficient statisticssufficientsufficiency
Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.
In statistics, a statistic is sufficient with respect to a statistical model and its associated unknown parameter if "no other statistic that can be calculated from the same sample provides any additional information as to the value of the parameter".

### Robust statistics

robustbreakdown pointrobustness
Important potential properties of statistics include completeness, consistency, sufficiency, unbiasedness, minimum mean square error, low variance, robustness, and computational convenience.
Robust statistics are statistics with good performance for data drawn from a wide range of probability distributions, especially for distributions that are not normal.

### Statistics

statisticalstatistical analysisstatistician
Statistics
Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.

### Well-behaved statistic

well behavior
Well-behaved statistic
First Definition: The variance of a well-behaved statistical estimator is finite and one condition on its mean is that it is differentiable in the parameter being estimated.

### Fisher information

information matrixinformationsingular statistical model
The most common is the Fisher information, which is defined on the statistic model induced by the statistic.
More generally, if T = t(X) is a statistic, then

### Function (mathematics)

functionfunctionsmathematical function
It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.

### Algorithm

algorithmscomputer algorithmalgorithm design
It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.

### Data set

datasetdatasetsdata
It is calculated by applying a function (statistical algorithm) to the values of the items of the sample, which are known together as a set of data.

### Statistical theory

statisticalstatistical theoriesmathematical statistics
More formally, statistical theory defines a statistic as a function of a sample where the function itself is independent of the sample's distribution; that is, the function can be stated before realization of the data.

### Descriptive statistics

descriptivedescriptive statisticstatistics
When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

### Estimation theory

parameter estimationestimationestimated
When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

### Statistical hypothesis testing

hypothesis testingstatistical teststatistical tests
When a statistic (a function) is being used for a specific purpose, it may be referred to by a name indicating its purpose: in descriptive statistics, a descriptive statistic is used to describe the data; in estimation theory, an estimator is used to estimate a parameter of the distribution (population); in statistical hypothesis testing, a test statistic is used to test a hypothesis.

### Arithmetic mean

meanaveragearithmetic
In calculating the arithmetic mean of a sample, for example, the algorithm works by summing all the data values observed in the sample and then dividing this sum by the number of data items.

### Data

In calculating the arithmetic mean of a sample, for example, the algorithm works by summing all the data values observed in the sample and then dividing this sum by the number of data items.

### Mean

mean valuepopulation meanaverage
The population mean is also a single measure; however, it is not called a statistic, because it is not obtained from a sample; instead it is called a population parameter, because it is obtained from the whole population.

### Quantile

quantilesquintiletertile
Sample quantiles besides the median, e.g., quartiles and percentiles

### Median

averagesample medianmedian-unbiased estimator
Sample quantiles besides the median, e.g., quartiles and percentiles Sample mean discussed in the example above and sample median

### Quartile

quartileslower quartilelower and upper quartiles
Sample quantiles besides the median, e.g., quartiles and percentiles