The population mean is the average value of every member of a statistical population. It is written with the Greek letter mu and, for a population of members, is calculated as:
Here is the value of the -th member. For a random quantity described by a probability distribution, the population mean is the same thing as its expected value. It is a fixed number, but unless the whole population is observed it must be estimated by the sample mean, which varies from sample to sample. The true average return of a share or strategy is a population mean that nobody observes, and the average of past returns is only an estimate of it. That estimate is imprecise: with a few years of data, the confidence interval around a mean return is typically wide enough to include zero. The law of large numbers states that the sample mean approaches the population mean as observations accumulate.