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The expected squared deviation from the mean, quantifying dispersion of a random variable.
DESCRIPTION
Variance measures how far values in a distribution spread around the mean. It equals the expected value of squared deviations and underpins many statistical techniques. Standard deviation is the square root of variance, restoring original units. In machine learning, high variance often indicates overfitting, while low variance indicates stability. Estimators differ for population versus sample variance, including Bessel’s correction. Variance composes mean squared error alongside bias.
ALTERNATIVE DEFINITIONS
Wikipedia
In probability theory and statistics, variance is the expectation of the squared deviation of a random variable from its mean.
Formal expectation-based definition linking to probability theory.
Encyclopaedia Britannica
Variance, in statistics, is a measure of the dispersion of a set of data points around their mean value.
Plain-language focus on dispersion around the mean.
OpenStax
Variance is the average of the squared differences from the mean and is the square of the standard deviation.
Educational framing connecting variance and standard deviation.
RELATED TERMS
Mean Standard Deviation Covariance Bias-Variance Tradeoff Population Variance Sample Variance Variance Analysis Mean Squared Error
COMPETING TERMS
KNOWLEDGE AREAS
Mathematics Data Science Testing & Validation
TARGET AUDIENCE
Data Scientist Data Analyst BI Specialist Information Analyst
EXTERNAL SOURCES
- Wikipedia - Variance
- NIST - Variance and dispersion overview
- OpenStax - Introductory textbook section
- Wikipedia - Context in model error decomposition
TOP QUESTIONS
Why is Variance important in statistics and ML?
Variance quantifies spread and stability of estimates, affecting confidence intervals and model generalization. It’s central to risk, noise, and overfitting analyses.
Category: Relevancy
What is the difference between Variance and Standard Deviation?
Variance is in squared units; standard deviation is its square root, restoring original units for interpretability.
Category: Comparison
What is Bessel’s correction in Variance calculations?
Using n−1 in the denominator produces an unbiased estimator of population variance from samples.
Category: Concept
How does Variance relate to Bias-Variance Tradeoff?
High-variance models overfit; low-variance models generalize more consistently. MSE decomposes into bias squared plus variance.
Category: Concept
When should I prefer robust measures over Variance?
With heavy-tailed or outlier-prone data, consider MAD or IQR. Variance is sensitive to outliers.
Category: Best Practice
How do I interpret a high Variance?
Data values are widely dispersed around the mean. In ML, it suggests model sensitivity to training fluctuations.
Category: Interpretation
Is Variance always nonnegative?
Yes. Being an expectation of squared deviations, variance cannot be negative.
Category: Fundamentals
How does sample size affect Variance estimation?
Smaller samples yield noisier variance estimates; larger samples stabilize estimates and reduce uncertainty.
Category: Testing
Can Variance be infinite?
Yes, heavy-tailed distributions like Cauchy have undefined variance. Always check distributional assumptions.
Category: Risks