The arithmetic mean of a random sample from a population. It is a statistic commonly used to estimate the population mean. Suppose there are n data, {x₁, x₂, … , xn}. The sample mean is (x₁ + x₂ + … + xn)/n. The expected value of the sample mean is the population mean. For sampling with replacement, the SE of the sample mean is the population standard deviation, divided by the square-root of the sample size. For sampling without replacement, the SE of the sample mean is the finite-population correction ((N−n)/(N−1))^½ times the SE of the sample mean for sampling with replacement, with N the size of the population and n the size of the sample.