Variance
Variance
Variance (/vɛərɪəns/; from Latin varians, meaning 'differing') is a statistical term that measures the dispersion of a set of data points around their mean value. It is a fundamental concept in probability theory and statistics.
Definition
In statistics, variance is the expectation of the squared deviation of a random variable from its mean. Informally, it measures how far a set of numbers are spread out from their average value. Variance is often denoted by the symbol σ².
Calculation
The variance of a random variable, statistical population, data set, or probability distribution is the average of the squared differences from the mean. The formula to calculate variance (σ²) is:
σ² = Σ ( X - μ )² / N
where:
- X represents each value in the dataset,
- μ is the mean of the dataset,
- N is the number of values in the dataset.
Related Terms
- Standard Deviation: The square root of the variance. It is a measure of the amount of variation or dispersion of a set of values.
- Mean: The average of a set of numbers.
- Probability Distribution: A mathematical function that provides the probabilities of occurrence of different possible outcomes in an experiment.
Applications
Variance is widely used in fields such as medicine, psychology, finance, and engineering to quantify variability or volatility. For example, in medicine, variance can be used to measure the variability in patients' responses to a certain treatment.
External links
- Medical encyclopedia article on Variance
- Wikipedia's article - Variance
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