The variance of a random variable X quantifies the spread or dispersion of the distribution of X. A random variable is essentially a function or rule that associates a number with the outcome of an experiment. Examples of random variables are an individual's weight, the number of inpatient admissions at a hospital on a single day, and a binary indicator (e.g., assigning values of 0 = no or 1 = yes) of whether or not a patient participating in a study had his or her conditions improve after taking a new drug.

The variance and its square root, the standard deviation, are important summary measures of the distribution of X and are essential for providing a complete description of X. Suppose that μX denotes the mean ...