# Variance vs. Variation: Know the Difference

By Shumaila Saeed || Updated on December 26, 2023

**Variance refers to the statistical measure of the spread of numbers in a dataset, whereas variation is the act or process of changing or the degree to which something changes.**

## Key Differences

Variance, in statistics, quantifies the degree to which numbers in a data set differ from the mean or average of the numbers. It is a numerical value that indicates the variability within a dataset. On the other hand, variation refers to the general concept of change or difference in conditions, situations, or physical characteristics. While variance is a specific statistical term with a precise mathematical definition, variation is a broader concept applicable in various contexts, including biology, music, and linguistics.

Shumaila Saeed

Dec 26, 2023

In the context of statistics, variance is calculated by averaging the squared differences from the mean, providing a measure of dispersion around the mean. It is a key concept in fields like finance, science, and engineering for assessing risk, reliability, and variability. Variation, however, encompasses any form of difference or deviation from a norm or standard. It's not confined to numerical data and can describe changes in patterns, behaviors, or physical traits across different entities or over time.

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Dec 26, 2023

Variance is often used in predictive models and analytics to determine the reliability of an expected result. A high variance indicates a wide spread of data points, suggesting less predictability. In contrast, variation is a more general term used to describe any form of difference, whether it's in language (linguistic variation), biological traits (genetic variation), or manufacturing processes (product variation). It does not imply a quantitative measure but rather a qualitative assessment of difference.

Shumaila Saeed

Dec 26, 2023

Furthermore, variance is an integral part of statistical hypothesis testing, where it helps in determining how significantly a result differs from a hypothesized value. It's a foundational element in the field of probability and statistics. Conversely, variation is a concept that cuts across multiple disciplines. In evolutionary biology, for instance, natural variation among organisms is a key principle, while in cultural studies, variations in social practices and norms are of interest.

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Dec 26, 2023

In summary, while variance is a specific, quantifiable concept in statistics representing the extent of dispersion in a dataset, variation is a broader term that encompasses any form of change, difference, or diversity in multiple contexts. Understanding the distinction between these terms is crucial for accurate communication and analysis in various academic and professional fields.

Shumaila Saeed

Dec 26, 2023

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## Comparison Chart

### Definition

A statistical measure of dispersion.

General concept of change or difference.

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### Context

Primarily used in statistics.

Used in various fields like biology, linguistics.

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### Quantitative/Qualitative

Quantitative measure.

Can be qualitative or quantitative.

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### Application

Used in data analysis, risk assessment.

Describes differences in characteristics, behaviors.

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### Representation

Represented numerically.

Described or observed, not necessarily numerical.

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## Variance and Variation Definitions

#### Variance

Variance measures how far a set of numbers are spread out from their average value.

The high variance in temperature readings complicates the prediction of weather patterns.

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#### Variation

In music, variation is a formal technique where material is repeated in an altered form.

The composer's variation on the theme brought a new dimension to the piece.

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#### Variance

Variance in finance refers to the volatility of an investment's returns over time.

The stock's high variance makes it a risky but potentially rewarding investment.

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#### Variation

Variation in linguistics refers to differences in pronunciation, grammar, or vocabulary among language users.

Regional variation in dialects can sometimes lead to miscommunication.

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#### Variance

Variance is the average of the squared differences from the Mean.

The variance in the test scores indicates a high disparity in student performance.

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#### Variance

Variance, in project management, is the difference between planned and actual performance.

The project's time variance showed we were two weeks behind schedule.

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#### Variation

The extent or degree to which something varies

A variation of ten pounds in weight.

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#### Variance

Variance in quality control indicates the degree of consistency in the manufacturing process.

The low variance in product dimensions ensures high-quality standards are maintained.

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#### Variation

Something different from another of the same type

Told a variation of an old joke.

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#### Variance

The state or quality of being variant or variable; variation

Considerable variance in temperature across the region.

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#### Variance

Difference or inconsistency

Your behavior is at variance with your beliefs.

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#### Variation

(Biology) The existence within a species or other group of organisms of differences in form, function, or behavior, especially when hereditary.

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#### Variance

The state or fact of being in disagreement or in conflict

I am at variance with her over who should pay for the damage.

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#### Variation

(Mathematics) A function that relates the values of one variable to those of other variables.

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#### Variance

A discrepancy between two statements or documents, especially between the charge in a criminal indictment and the evidence presented.

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#### Variation

A form that is an altered version of a given theme, diverging from it by melodic ornamentation and by changes in harmony, rhythm, or key.

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#### Variance

An exception to the application of a usual rule, granted by an authority on the basis of hardship or practicality

A zoning variance.

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#### Variance

(Chemistry) The number of thermodynamic variables, such as temperature and pressure, required to specify a state of equilibrium of a system, given by the phase rule; the degrees of freedom of a system.

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#### Variation

The act of varying; a partial change in the form, position, state, or qualities of a thing.

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#### Variation

A related but distinct thing.

When the process didn't work, we tried a variation.

All of his soups are variations on a single recipe.

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#### Variance

A difference between what is expected and what is observed; deviation.

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#### Variation

(nautical) The angular difference at the vessel between the direction of true north and magnetic north.

Magnetic declination

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#### Variance

An official permit to do something that is ordinarily forbidden by regulations.

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#### Variation

(music) A technique where material is repeated with alterations to the melody, harmony, rhythm, timbre, texture, counterpoint or orchestration; but with some invariant characteristic, e.g. a ground bass.

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#### Variance

(law) A departure from a cause of action originally in a complaint.

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#### Variation

The act of varying; a partial change in the form, position, state, or qualities of a thing; modification; alteration; mutation; diversity; deviation; as, a variation of color in different lights; a variation in size; variation of language.

The essences of things are conceived not capable of any such variation.

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#### Variation

Extent to which a thing varies; amount of departure from a position or state; amount or rate of change.

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#### Variance

Covariance and contravariance generally.

Depending on the variance of the type constructor, the subtyping relation of the simple types may be either preserved, reversed, or ignored for the respective complex types.

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#### Variation

Change of termination of words, as in declension, conjugation, derivation, etc.

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#### Variance

The quality or state of being variant; change of condition; variation.

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#### Variation

Repetition of a theme or melody with fanciful embellishments or modifications, in time, tune, or harmony, or sometimes change of key; the presentation of a musical thought in new and varied aspects, yet so that the essential features of the original shall still preserve their identity.

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#### Variance

Difference that produces dispute or controversy; disagreement; dissension; discord; dispute; quarrel.

That which is the strength of their amity shall prove the immediate author of their variance.

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#### Variation

One of the different arrangements which can be made of any number of quantities taking a certain number of them together.

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#### Variance

A disagreement or difference between two parts of the same legal proceeding, which, to be effectual, ought to agree, - as between the writ and the declaration, or between the allegation and the proof.

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#### Variance

The expected value of the square of the deviation from the mean of a randomly distributed variable; the second moment about the mean. This is also the square of the standard deviation.

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#### Variation

An activity that varies from a norm or standard;

Any variation in his routine was immediately reported

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#### Variation

A repetition of a musical theme in which it is modified or embellished

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#### Variation

Something a little different from others of the same type;

An experimental version of the night fighter

An emery wheel is a modern variant of the grindstone

The boy is a younger edition of his father

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#### Variance

The second moment around the mean; the expected value of the square of the deviations of a random variable from its mean value

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#### Variation

An artifact that deviates from a norm or standard;

He patented a variation on the sandal

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#### Variance

A difference between conflicting facts or claims or opinions;

A growing divergence of opinion

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#### Variation

The angle (at a particular location) between magnetic north and true north

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#### Variation

(astronomy) any perturbation of the mean motion or orbit of a planet or satellite (especially a perturbation of the earth's moon)

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#### Variance

An activity that varies from a norm or standard;

Any variation in his routine was immediately reported

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#### Variation

(biology) an organism that has characteristics resulting from chromosomal alteration

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#### Variation

The act of changing or altering something slightly but noticeably from the norm or standard;

Who is responsible for these variations in taxation?

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#### Variation

Variation refers to the occurrence of an organism, trait, or gene in more than one form.

Genetic variation in the population leads to diverse physical characteristics.

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#### Variation

Variation is the act or process of changing or altering.

The variation in her teaching methods keeps the students engaged.

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#### Variation

Variation in art refers to the use of different techniques or styles in an artist's work.

His variation in painting styles showcases his versatility as an artist.

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## Repeatedly Asked Queries

#### Is variance the same as standard deviation?

No, standard deviation is the square root of variance.

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#### What does high variance indicate?

High variance indicates a wide spread of data points around the mean.

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#### Can variance be negative?

No, variance is always non-negative as it's based on squared values.

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#### How does variation contribute to evolution?

Genetic variation is crucial for natural selection and evolutionary processes.

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#### What is variance?

Variance is a statistical measure of the dispersion of a set of data points.

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#### How does variance relate to hypothesis testing?

Variance helps determine the significance of differences in statistical tests.

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#### What is variation?

Variation refers to the concept of change or differences in conditions, traits, or behaviors.

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#### How is variance calculated?

Variance is calculated as the average of the squared differences from the mean.

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#### Can variance be applied to non-numerical data?

No, variance applies to numerical datasets.

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#### What role does variation play in art?

Variation in art allows for diverse expressions and styles.

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#### Is variation always a natural occurrence?

Variation can be natural or induced by external factors.

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#### Can variation be measured?

Variation can be qualitative or quantitative, depending on the context.

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#### Is variation important in education?

Yes, variation in teaching methods can enhance learning and engagement.

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#### What is the importance of variance in finance?

Variance in finance indicates the volatility or risk of an investment.

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#### How does linguistic variation manifest?

Linguistic variation appears in different dialects, accents, and usage among speakers.

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#### What is the impact of variation in manufacturing?

Variation in manufacturing affects product consistency and quality.

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#### What is an example of cultural variation?

Cultural variation includes differences in traditions, customs, and beliefs among societies.

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#### How does variance affect data interpretation?

High variance can indicate less predictability and reliability in data interpretation.

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#### Can variation occur in non-biological contexts?

Yes, variation can occur in language, culture, art, and other areas.

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#### Can variance be zero?

Yes, if all data points are the same, variance is zero.

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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.