In probability theory and statistics, the variance of a random variable (or somewhat more precisely, of a probability distribution) is a measure of its statistical dispersion, indicating how its possible values are spread around the expected value. While the expected value shows the location of the distribution, the variance indicates the variability of the values. A more understandable measure is the square root of the variance, called the standard deviation. As its name implies it gives in a standard form an indication of the usual deviations from the mean.
The variance of a real-valued random variable is its second central moment, and it also happens to be its second cumulant.