  # Variance vs. Standard Deviation: What's the Difference? Edited by Sumera Saeed || By Sawaira Riaz || Updated on November 18, 2023
"Variance" measures the average squared deviation from the mean, while "Standard Deviation" is the square root of variance, indicating data spread. ## Key Differences

"Variance" is a statistical metric that quantifies the average squared differences from the mean of a data set. It provides insights into the dispersion or spread of data points. In contrast, the "Standard Deviation" is simply the square root of variance, offering a more interpretable measure of data spread since it's in the original units of the data.
When analyzing "Variance," higher values signify that data points deviate more from the average, implying greater dispersion. On the other hand, "Standard Deviation" gives a direct sense of how far, on average, data points are from the mean, serving as a more intuitive descriptor of variability.
The primary advantage of "Variance" is that it's derived directly from data differences, making it a foundational concept in statistics. However, since it's in squared units, it can sometimes be challenging to interpret in context. This is where the "Standard Deviation" becomes valuable, as it provides variability context in the same unit as the data itself.
Both "Variance" and "Standard Deviation" are pivotal in fields like finance, economics, and psychology to understand data variability. While "Variance" offers a raw measure of dispersion, "Standard Deviation" refines it, offering clearer, actionable insights about data spread.

## Comparison Chart

### Definition

Average of squared differences from the mean.
Square root of variance.

### Units

Squared units of data.
Original units of data.

### Interpretation Difficulty

Somewhat challenging due to squared units.
Easier, given it's in original data units.

### Application

Fundamental in statistical analysis.
More commonly used due to interpretability.

### Relation to Mean

Provides squared deviation from mean.
Directly indicates average distance from mean.

## Variance and Standard Deviation Definitions

#### Variance

Average of the squared differences from the mean.
The high Variance indicated a wide dispersion in the data set.

#### Standard Deviation

Measure reflecting the average deviation from the mean.
The Standard Deviation of exam scores helped educators identify curriculum effectiveness.

#### Variance

Quantifies how far data points are spread out from their average value.
The stock returns had a low Variance, implying stable performance.

#### Standard Deviation

Gauge of uncertainty or variability in a data set.
Researchers noted a minimal Standard Deviation in the experimental results.

#### Variance

Statistical metric of data point deviations from the mean in squared units.
The Variance of house prices in the region was significant due to varied property types.

#### Standard Deviation

Square root of variance, showing data spread.
The low Standard Deviation indicated closely clustered data points.

#### Variance

Reflects the consistency or variability of a set of numbers.
The Variance in annual rainfall was used to predict droughts.

#### Standard Deviation

Average distance of data points from the mean.
Given the high Standard Deviation, investors were advised to be cautious.

#### Variance

The state or quality of being variant or variable; variation
Considerable variance in temperature across the region.

#### Standard Deviation

Indicator of data variability in original units.
Despite similar averages, City A had a greater Standard Deviation in temperatures than City B.

#### Variance

Difference or inconsistency

#### 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.

#### Variance

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

#### Variance

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

#### Variance

(Statistics) The square of the standard deviation.

#### 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.

#### Variance

The act of varying or the state of being variable.

#### Variance

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

#### Variance

The state of differing or being in conflict.

#### Variance

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

#### Variance

(law) A discrepancy between two legal documents.

#### Variance

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

#### Variance

(statistics) The second central moment in probability.

#### Variance

The number of degrees of freedom in a system.

#### 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.

#### Variance

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

#### 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.

#### 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.

#### 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.

#### Variance

An event that departs from expectations

#### Variance

Discord that splits a group

#### Variance

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

#### Variance

A difference between conflicting facts or claims or opinions;
A growing divergence of opinion

#### Variance

The quality of being subject to variation

#### Variance

An activity that varies from a norm or standard;
Any variation in his routine was immediately reported

#### Variance

Measure of data dispersion in squared terms.
Despite many data points, the Variance was surprisingly low.

## FAQs

#### How does squaring differences in "Variance" calculations help?

Squaring in "Variance" eliminates negative deviations and emphasizes larger differences.

#### Is "Standard Deviation" always non-negative?

Yes, "Standard Deviation" is always non-negative as it's the square root of variance.

#### How is "Variance" calculated in a dataset?

"Variance" is computed as the average of squared differences from the mean.

#### Is "Standard Deviation" affected by outliers?

Yes, "Standard Deviation" can be significantly affected by outliers, as can "Variance."

#### What is the primary difference between "Variance" and "Standard Deviation"?

"Variance" is in squared units, while "Standard Deviation" is in the original data units.

#### Why might a researcher choose "Standard Deviation" over "Variance"?

"Standard Deviation" offers clearer interpretability in many contexts compared to "Variance."

#### Can both "Variance" and "Standard Deviation" be zero?

Yes, both can be zero, indicating no variability in the dataset.

#### Which measure, "Variance" or "Standard Deviation," is more interpretable?

"Standard Deviation" is more interpretable due to its original data units.

#### In what scenarios is "Variance" particularly useful?

"Variance" is foundational in many statistical methods and theories, making it essential in advanced analyses.  