variance
Sign in to savethumb|400px|right|Example of samples from two populations with the same mean but different variances. The red population has mean and variance (), while the blue population has mean and variance ().
AI overview
Variance measures how spread out data points are from their average—a small variance means numbers cluster close together, while a large variance means they're scattered far apart. It matters because two groups can have the same average but tell very different stories; for example, one group's values might be tightly bunched while another's are wildly scattered, which affects how predictable or stable that group is.
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Article
50 sectionsContents
- Definition
- Discrete random variable
- Absolutely continuous random variable
- Examples
- Exponential distribution
- Fair die <!--Singular: die; plural: dice. Don't change-->
- Commonly used probability distributions
- Properties
- Basic properties
- Issues of finiteness
- Decomposition
- Calculation from the CDF
- Characteristic property
- Units of measurement
- Propagation
- Addition and multiplication by a constant
- Linear combinations
- Matrix notation for the variance of a linear combination
- Sum of variables
- Sum of uncorrelated variables
- Sum of correlated variables
- Sum of correlated variables with fixed sample size
- Sum of uncorrelated variables with random sample size
- Weighted sum of variables
- Product of variables
- Product of independent variables
- Product of statistically dependent variables
- Arbitrary functions
- Population variance and sample variance
- Population variance
- Sample variance
- Biased sample variance
- Unbiased sample variance
- Example
- Distribution of the sample variance
- Samuelson's inequality
- Effect of adding one observation on variance
- Relations with the harmonic and arithmetic means
- Tests of equality of variances
- Moment of inertia
- Semivariance
- Etymology
- Generalizations
- For complex variables
- For vector-valued random variables
- As a matrix
- As a scalar
- See also
- Types of variance
- References
thumb|400px|right|Example of samples from two populations with the same mean but different variances. The red population has mean and variance (), while the blue population has mean and variance ().
In probability theory and statistics, variance is the expected value of the squared deviation from the mean of a random variable. The standard deviation is obtained as the square root of the variance. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers are spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , {{tmath|\operatorname{Var}(X)}}, , or {{tmath|\mathbb{V}(X)}}.