Statistic vs. Parameter — What's the Difference?

A numerical value that describes a characteristic of a sample.

Used in defining the theoretical framework of statistical models.

Calculated from a subset of the population.

Represents the true state of a population.

Varies from sample to sample.

A numerical value summarizing a characteristic for an entire population.

Used in making inferences about a population.

Fixed and does not vary unless the population itself changes.

Helps in hypothesis testing.

Often estimated via statistics due to practical constraints.

A statistic (singular) or sample statistic is any quantity computed from values in a sample which is considered for a statistical purpose. Statistical purposes include estimating a population parameter, describing a sample, or evaluating a hypothesis.

A parameter (from the Ancient Greek παρά, para: "beside", "subsidiary"; and μέτρον, metron: "measure"), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when identifying the system, or when evaluating its performance, status, condition, etc.

A fact or piece of data obtained from a study of a large quantity of numerical data

A numerical or other measurable factor forming one of a set that defines a system or sets the conditions of its operation

Another term for statistical

A limit or boundary which defines the scope of a particular process or activity

A numerical piece of information.

A constant in an equation that varies in other equations of the same general form, especially such a constant in the equation of a curve or surface that can be varied to represent a family of curves or surfaces.

A calculated numerical value (such as the sample mean) that characterizes some aspect of a sample set of data, and that is often meant to estimate the true value of a corresponding parameter (such as the population mean) in an underlying population.

One of a set of independent variables that express the coordinates of a point.

One viewed solely as a piece of statistical or numerical information

One of a set of measurable factors, such as temperature and pressure, that define a system and determine its behavior and are varied in an experiment.

Alternative form of statistical

Usage Problem A factor that restricts what is possible or what results

A single item in a statistical study.

A factor that determines a range of variations; a boundary

A quantity calculated from the data in a sample, which characterises an important aspect in the sample (such as mean or standard deviation).

(Statistics) A quantity, such as a mean, that is calculated from data and describes a population.

A person, or personal event, reduced to being an item of statistical information.

Usage Problem A distinguishing characteristic or feature.

Of or pertaining to statistics; as, statistical knowledge; statistical tabulation.

A value kept constant during an experiment, equation, calculation, or similar, but varied over other versions of the experiment, equation, calculation, etc.

A datum that can be represented numerically

(sciences) A variable that describes some system (material, object, event, etc.) or some aspect thereof.

(statistics) Any measured quantity of a statistical population that summarises or describes an aspect of the population.

(machine learning) A variable of a model that is trained by a machine learning algorithm.

(programming) An input variable of a function definition, that gets an actual value (argument) at execution time.

An actual value given to such a formal parameter.

A characteristic or feature that distinguishes something from others.

(geometry) In the ellipse and hyperbola, a third proportional to any diameter and its conjugate, or in the parabola, to any abscissa and the corresponding ordinate.

(crystallography) The ratio of the three crystallographic axes which determines the position of any plane.

(crystallography) The fundamental axial ratio for a given species.

A constant number which is part of a theory, function, or calculation, whose value is not determined by the form of the theory or equation itself, and may in some cases be arbitrary assigned.

A term applied to some characteristic magnitude whose value, invariable as long as one and the same function, curve, surface, etc., is considered, serves to distinguish that function, curve, surface, etc., from others of the same kind or family.

Any constant number which is required to calculate values of observed phenomena according to a theory, but the value of which must be determined by experiment, and cannot be calculated from the fundamental assumptions of the theory. In general, a theory which has a large number of parameters, though it may accurately predict experimental results, is considered as having less explanatory power and as being less esthetically pleasing than a theory with fewer parameters.

The ratio of the three crystallographic axes which determines the position of any plane; also, the fundamental axial ratio for a given species.

The limits, guidelines, or assumptions from within which an activity is carried out; as, new arrivals need to learn the parameters of the research in our department.

A variable used in a calculation within a computer program which must be assigned a value before the calculation can be performed; as, let's plug in the parameters and see what the result is.

A characteristic or element, especially one used as a criterion for evaluation or judgment; as, a useful parameter for determining efficiency.

A constant in the equation of a curve that can be varied to yield a family of similar curves

Any factor that defines a system and determines (or limits) its performance

A quantity (such as the mean or variance) that characterizes a statistical population and that can be estimated by calculations from sample data

A measure derived from a subset of data (sample) to estimate characteristics of a larger population.

Parameters can be calculated directly only when full population data is available, which is rare in large populations.

Statistics vary with samples and are used for estimation; parameters are fixed values describing the whole population.

Increasing sample size and using better sampling methods can improve the accuracy of statistics in estimating parameters.

Statistics provide an estimate that can vary due to sample size and selection but are designed to be as representative as possible.

Researchers use statistics when full population data is unavailable and parameters when it is accessible.

A measure that describes the true characteristic of an entire population.

Gathering data from an entire population is often impractical, so statistics provide a feasible approximation.

The average income of sampled households in a study is a statistic.

The actual average temperature of an area, if known from complete data, is a parameter.

Understanding parameters helps in making accurate predictions and decisions based on the true characteristics of a population.

Statistics help in making inferences or testing hypotheses about population parameters.

A larger sample size generally provides statistics that are better estimators of the population parameters.

Statistics do not become parameters; they are estimates used to infer parameters.

Errors in sample data can lead to inaccurate statistics, misleading about the true population parameters.