variance was first introduced by Ronald Fisher in his 1918 paper The Correlation Between Relatives on the Supposition of Mendelian Inheritance: The great body of available statistics show us that the deviations of a human measurement from its mean follow very closely the Normal Law of Errors, and, therefore, that the variability may be uniformly measured by the standard deviation corresponding to the square root of the mean square error. When there are two independent causes of variability capable of producing in an otherwise uniform population distributions with standard deviations and , it is found that the distribution, when both causes act together, has a standard deviation . It is therefore desirable in analysing the causes of variability to deal with the square of the standard deviation as the measure of variability. We shall term this quantity the Variance... Definition The variance of a random variable is the expected value of the squared deviation from the mean of , : This definition encompasses random variables that are generated by processes that are discrete, continuous, neither, or mixed. The variance can also be thought of as the covariance of a random variable with itself: The variance is also equivalent to the second cumulant of a probability distribution that generates . The variance is typically designated as , or sometimes as or , or symbolically as or simply (pronounced "sigma squared"). The expression for the variance can be expanded as follows: In other words, the variance of is equal to the mean of the square of minus the square of the mean of . This equation should not be used for computations using floating point arithmetic, because it suffers from catastrophic cancellation if the two components of the equation are similar in magnitude. For other numerically stable alternatives, see Algorithms for calculating variance. Discrete random variable If the generator of random variable is discrete with probability mass function , then where is the expected value. That is, (When such a discrete weighted variance is specified by weights whose sum is not 1, then one divides by the sum of the weights.) The variance of a collection of equally likely values can be written as where is the average value. That is, The variance of a set of equally likely values can be equivalently expressed, without directly referring to the mean, in terms of squared deviations of all pairwise squared distances of points