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.

1

Wikipedia contributors. (2021, March 2). Variance. Wikipedia. https://en.wikipedia.org/wiki/Variance