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The arithmetic mean (or simply mean or average) of a list of numbers, is the sum of all of the numbers divided by their count.Similarly, the mean of a sample ,, …,, usually denoted by ¯, is the sum of the sampled values divided by the number of items in the sample.
In calculus, and especially multivariable calculus, the mean of a function is loosely defined as the average value of the function over its domain. In one variable, the mean of a function f ( x ) over the interval ( a , b ) is defined by: [ 1 ]
The arithmetic mean of a population, or population mean, is often denoted μ. [2] The sample mean ¯ (the arithmetic mean of a sample of values drawn from the population) makes a good estimator of the population mean, as its expected value is equal to the population mean (that is, it is an unbiased estimator).
The arithmetic mean, or less precisely the average, of a list of n numbers x 1, x 2, . . . , x n is the sum of the numbers divided by n: + + +. The geometric mean is similar, except that it is only defined for a list of nonnegative real numbers, and uses multiplication and a root in place of addition and division:
The geometric mean is more appropriate than the arithmetic mean for describing proportional growth, both exponential growth (constant proportional growth) and varying growth; in business the geometric mean of growth rates is known as the compound annual growth rate (CAGR). The geometric mean of growth over periods yields the equivalent constant ...
The arithmetic mean can be similarly defined for vectors in multiple dimensions, not only scalar values; this is often referred to as a centroid. More generally, because the arithmetic mean is a convex combination (meaning its coefficients sum to ), it can be defined on a convex space, not only a vector space.