# Statistic vs. Parameter: Know the Difference

By Shumaila Saeed || Updated on December 25, 2023

**"Statistic" refers to a numerical measure calculated from a sample, while a "parameter" is a numerical characteristic that describes a population as a whole.**

## Key Differences

A statistic is a numerical value that describes a characteristic of a sample, a subset of a larger population. In contrast, a parameter is a numerical value that describes a characteristic of an entire population.

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Statistics are derived from sample data and are used to estimate or infer information about the population. Parameters are fixed values that precisely describe a population, but are often unknown and estimated by statistics.

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The calculation of a statistic involves data from a sample, which can be subject to sampling variability. Parameters, however, represent the true value within the population and remain constant.

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Statistics are practical in research when it is impractical or impossible to study an entire population. Parameters, while being the ultimate target of estimation, often remain theoretical in large populations.

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Examples of statistics include sample mean and sample standard deviation. Parameters are exemplified by population mean and population standard deviation, providing a more comprehensive picture.

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## Comparison Chart

### Purpose

Used for inference about the population.

Represents a true population characteristic.

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## Statistic and Parameter Definitions

#### Statistic

A figure used for inferential purposes in research.

The researcher used the statistic to estimate population trends.

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#### Parameter

A numerical characteristic of a population.

The population's average income is an important parameter.

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#### Statistic

An empirical value used in statistical analysis.

The calculated statistic was crucial for the study's conclusions.

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#### Parameter

A fixed, often theoretical, value in statistics.

In this model, the growth rate is a key parameter.

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#### Statistic

A numerical value representing a sample characteristic.

The statistic showed a decrease in unemployment rates.

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#### Parameter

An underlying characteristic that statistics estimate.

The parameter of interest was the overall infection rate.

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#### Parameter

A constant value in the field of statistics.

The parameter was used to validate the statistical model.

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#### Statistic

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.

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#### Parameter

A theoretical measure for a total population.

The true mean is a parameter that the study aimed to estimate.

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#### Statistic

One viewed solely as a piece of statistical or numerical information

Got laid off and became another statistic in the slumping economy.

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#### Parameter

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.

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#### Parameter

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

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#### Parameter

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.

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#### Statistic

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

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#### Parameter

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

"all the parameters of shelter—where people will live, what mode of housing they will choose, and how they will pay for it" (New York).

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#### Statistic

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

By dying from an overdose, he became just another statistic.

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#### Parameter

A factor that determines a range of variations; a boundary

An experimental school that keeps expanding the parameters of its curriculum.

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#### Statistic

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

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#### Parameter

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

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#### Statistic

A measure calculated from sample data.

The average age in the survey results is a useful statistic.

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#### Parameter

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

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#### Statistic

A variable measure reflecting a subset of data.

This year's team performance statistic is impressive.

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#### Parameter

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

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#### Parameter

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

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#### Parameter

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

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#### Parameter

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

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#### Parameter

A characteristic or feature that distinguishes something from others.

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#### Parameter

(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.

The parameter of the principal axis of a conic section is called the latus rectum.

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#### Parameter

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

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#### Parameter

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

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#### Parameter

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.

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#### Parameter

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.

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#### Parameter

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.

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#### Parameter

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

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#### Parameter

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.

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#### Parameter

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.

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#### Parameter

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

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#### Parameter

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

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#### Parameter

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

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#### Parameter

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

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## Repeatedly Asked Queries

#### Why are parameters often unknown?

Parameters are often unknown because it's usually impractical to measure an entire population.

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#### What is a statistic?

A statistic is a numerical value calculated from a sample data set.

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#### Can a statistic be used to estimate a parameter?

Yes, statistics are often used to estimate the corresponding parameters of a population.

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#### How is a statistic different from a parameter?

A statistic is variable and estimated from a sample, while a parameter is a fixed value describing a population.

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#### What is a parameter?

A parameter is a numerical characteristic of an entire population.

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#### Why do researchers use statistics?

Researchers use statistics to make inferences about a population based on sample data.

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#### What is the importance of knowing a parameter?

Knowing a parameter helps in understanding the true characteristic of a population.

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#### Is a statistic always accurate?

Statistics are subject to sampling variability and may not always accurately represent the population.

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#### What's an example of a parameter?

An example of a parameter is the average height of all students in a school.

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#### Are parameters used in hypothesis testing?

Parameters are the values being tested against in hypothesis testing.

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#### How is the population mean different from the sample mean?

The population mean (a parameter) is the average of all data points in the population, while the sample mean (a statistic) is the average of data points in a sample.

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#### Why are parameters considered theoretical?

Parameters are considered theoretical because they describe an entire population, which is often not fully observable.

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#### How do sample size and statistic relate?

The size of a sample can affect the accuracy of the statistic as an estimate of the population parameter.

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#### What role do parameters play in statistical models?

Parameters are the values that statistical models aim to estimate or predict.

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#### What's an example of a statistic?

An example of a statistic is the average height of students in a classroom.

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#### Is parameter estimation always possible?

Parameter estimation is often possible but can be challenging in large or inaccessible populations.

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#### How do statisticians calculate statistics?

Statisticians calculate statistics using sample data and statistical formulas or software.

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#### Can parameters vary over time?

While parameters are fixed for a given population at a specific time, they can vary over time as the population changes.

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#### Are statistics limited to quantitative data?

Statistics are primarily used with quantitative data, but some statistical techniques can handle qualitative data.

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#### Can a statistic become a parameter?

A statistic cannot become a parameter, as they inherently describe different data sets (sample vs. population).

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About Author

Written by

Shumaila SaeedShumaila Saeed, an expert content creator with 6 years of experience, specializes in distilling complex topics into easily digestible comparisons, shining a light on the nuances that both inform and educate readers with clarity and accuracy.