Glossary
Variance
Variance is the arithmetic mean of the squared deviations from the mean. It measures the average squared distance of each data point from the centre of the distribution, providing a numerical summary of how spread out the data are.
Definition
Variance is the arithmetic mean of the squared deviations from the mean. It measures the average squared distance of each data point from the centre of the distribution, providing a numerical summary of how spread out the data are.
Why It Matters
Variance is the foundational measure of dispersion from which the standard deviation is derived. It plays a central role in ANOVA (where "Analysis of Variance" literally partitions variance into components), in regression (where R² represents explained variance), and in portfolio theory (where variance measures investment risk). Because it is expressed in squared units, the standard deviation is often preferred for interpretation.
Example
Two investment funds both have an average annual return of 7%. Fund A has a variance of 4 (standard deviation = 2%), while Fund B has a variance of 100 (standard deviation = 10%). Although both funds offer the same average return, Fund B is far riskier because its returns fluctuate wildly around the mean. A risk-averse investor would prefer Fund A.
Related Terms
- Standard Deviation (the square root of variance)
- Mean
- Normal Distribution
- ANOVA
- Effect Size
Software Notes
- SPSS: Analyze > Descriptive Statistics > Frequencies or Descriptives. Check "Variance" under Statistics.
- R:
var(x, na.rm = TRUE)computes the sample variance.var(x, na.rm = TRUE) * (length(x)-1) / length(x)for population variance. - Stata:
summarize varname, detailreports variance in the "Variance" row.