Variance
Understanding variance in statistics
What is variance?
Variance is a measure of dispersion that describes how far values in a dataset are spread out from the mean. A higher variance indicates greater variability.
Variance formula
Variance is calculated as the average of the squared differences between each value and the mean.
Population variance: σ² = Σ(x − μ)² / N
Sample variance: s² = Σ(x − x̄)² / (n − 1)
Example
Dataset: 2, 4, 6
Mean = 4
Squared differences:
(2 − 4)² = 4
(4 − 4)² = 0
(6 − 4)² = 4
Variance = (4 + 0 + 4) / 3 = 2.67
Why is variance important?
Variance helps quantify variability and risk. It is widely used in statistics, finance, and data analysis to compare distributions and understand uncertainty.
Variance vs standard deviation
Variance is expressed in squared units, which can be unintuitive. Standard deviation is the square root of variance and is easier to interpret in real-world contexts.