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  2. Geometric mean - Wikipedia

    en.wikipedia.org/wiki/Geometric_mean

    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 ...

  3. Gauss–Legendre algorithm - Wikipedia

    en.wikipedia.org/wiki/Gauss–Legendre_algorithm

    The arithmetic–geometric mean of two numbers, a 0 and b 0, is found by calculating the limit of the sequences + = +, + =, which both converge to the same limit. If = and = ⁡ then the limit is (⁡) where () is the complete elliptic integral of the first kind

  4. List of price index formulas - Wikipedia

    en.wikipedia.org/wiki/List_of_price_index_formulas

    The change in a Fisher index from one period to the next is the geometric mean of the changes in Laspeyres' and Paasche's indices between those periods, and these are chained together to make comparisons over many periods: = This is also called Fisher's "ideal" price index.

  5. AM–GM inequality - Wikipedia

    en.wikipedia.org/wiki/AM–GM_inequality

    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:

  6. Generalized mean - Wikipedia

    en.wikipedia.org/wiki/Generalized_mean

    In mathematics, generalized means (or power mean or Hölder mean from Otto Hölder) [1] are a family of functions for aggregating sets of numbers. These include as special cases the Pythagorean means ( arithmetic , geometric , and harmonic means ).

  7. Arithmetic–geometric mean - Wikipedia

    en.wikipedia.org/wiki/Arithmetic–geometric_mean

    In mathematics, the arithmetic–geometric mean (AGM or agM [1]) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means. The arithmetic–geometric mean is used in fast algorithms for exponential , trigonometric functions , and other special functions , as well as some ...

  8. QM-AM-GM-HM inequalities - Wikipedia

    en.wikipedia.org/wiki/QM-AM-GM-HM_Inequalities

    In mathematics, the QM-AM-GM-HM inequalities, also known as the mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean square). Suppose that ,, …, are positive real numbers. Then

  9. Pythagorean means - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_means

    Nomograms to graphically calculate arithmetic (1), geometric (2) and harmonic (3) means, z of x=40 and y=10 (red), and x=45 and y=5 (blue) Of all pairs of different natural numbers of the form ( a , b ) such that a < b , the smallest (as defined by least value of a + b ) for which the arithmetic, geometric and harmonic means are all also ...