population mean

The average value of some variable that is measured for all members of a (possibly infinite) population. If the value of the variable for a randomly chosen member of the population is denoted by X, then the population mean is the expectation of X and is usually denoted by μ (the notation μ was introduced in 1936 by Sir Ronald Fisher in the sixth edition of his Statistical Methods for Research Workers). Similarly, the population variance, usually denoted by σ², is the mean of the squared differences between the values of the members of the population and the population mean: this is the expectation of (X−μ)².