 The arithmetic mean of a set of numbers "x"1, "x"2, ..., "xn" is typically denoted by formula_1.If the data set were based on a series of observations obtained by sampling from a statistical population, the arithmetic mean is the sample mean (denoted formula_1) to distinguish it from the mean of the underlying distribution, the population mean (denoted formula_3 or formula_4).In probability and statistics, the population mean, or expected value, is a measure of the central tendency either of a probability distribution or of the random variable characterized by that distribution.