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  2. 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:

  3. Arithmetic–geometric mean - Wikipedia

    en.wikipedia.org/wiki/Arithmeticgeometric_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 ...

  4. Geometric mean - Wikipedia

    en.wikipedia.org/wiki/Geometric_mean

    The geometric mean of a data set is less than the data set's arithmetic mean unless all members of the data set are equal, in which case the geometric and arithmetic means are equal. This allows the definition of the arithmetic-geometric mean, an intersection of the two which always lies in between.

  5. 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

  6. Pythagorean means - Wikipedia

    en.wikipedia.org/wiki/Pythagorean_means

    A geometric construction of the quadratic mean and the Pythagorean means (of two numbers a and b). Harmonic mean denoted by H, geometric by G, arithmetic by A and quadratic mean (also known as root mean square) denoted by Q. Comparison of the arithmetic, geometric and harmonic means of a pair of numbers.

  7. List of mathematical constants - Wikipedia

    en.wikipedia.org/wiki/List_of_mathematical_constants

    where agm is the arithmetic–geometric mean and is the lemniscate constant. 1799 [31] ? Second Hermite constant [32] 1.15470 05383 79251 52901 [Mw 20] [OEIS 25] 1822 to 1901 Liouville's constant [33]

  8. Atkinson index - Wikipedia

    en.wikipedia.org/wiki/Atkinson_index

    The Atkinson index is defined as: (, …,) = {(=) / (=) / = (,...,) = +where is individual income (i = 1, 2, ..., N) and is the mean income.. In other words, the Atkinson index is the complement to 1 of the ratio of the Hölder generalized mean of exponent 1−ε to the arithmetic mean of the incomes (where as usual the generalized mean of exponent 0 is interpreted as the geometric mean).

  9. List of price index formulas - Wikipedia

    en.wikipedia.org/wiki/List_of_price_index_formulas

    The Törnqvist or Törnqvist-Theil index is the geometric average of the n price relatives of the current to base period prices (for n goods) weighted by the arithmetic average of the value shares for the two periods. [16] [17]