Statistics
Variance
The average of the squared differences between each data point and the mean.
What is Variance?
Variance is a fundamental measure of statistical dispersion that quantifies how far a set of numbers spread out from their average value. Because differences are squared, variance gives more weight to extreme deviations and is expressed in squared units of the original data.
Why Variance Matters
Variance is a core mathematical concept underlying almost all inferential statistics, allowing researchers to partition the total variability in an outcome into 'explained' and 'unexplained' portions.
Example
A researcher calculates the variance of test scores to determine how tightly clustered students' performance is around the class average. A high variance indicates widely differing skill levels.
Common Mistakes
- Attempting to interpret variance in the original units of measurement, forgetting that the calculation involves squaring the differences.
- Failing to distinguish between population variance and sample variance.