Mean (Statistics)

The mean, in statistics, is the average of a set of numbers, found by adding them up and dividing by how many there are:

Here $x_i$ are the values and $n$ is their number. This arithmetic mean is the most common measure of the centre of a data set, alongside the median and the mode. A mean computed from a sample is the sample mean, used to estimate the population mean, and the mean of a probability distribution is its expected value. In finance the mean of past returns is the usual estimate of a typical period's return, though one extreme value can distort it. For growth over several periods the geometric mean is the right measure. A gain of 50 percent followed by a loss of 50 percent has an arithmetic mean of zero, yet 100 becomes 75, a geometric mean of about -13.4 percent per period. A weighted average gives some values more influence than others.