The variance of a variable $X$ refers to the expectation value of the squared difference between $X$ and its mean.1 In other words, it is a measure of how much a set of data is spread around its average.

In the discrete case, a variable $X$ with Probability mass function $p$ has the variance:

$$ \text{Var}(X) = \sum_{i = 1}^N p_i\cdot(x_i - \mu)^2 ,$$

where $\mu$ is the mean.


Wikipedia contributors. (2021, March 2). Variance. Wikipedia.