Search results
Results From The WOW.Com Content Network
The geometric mean of the three numbers is the cube root of their product, for example with numbers , , and , the geometric mean is = =. The geometric mean is useful whenever the quantities to be averaged combine multiplicatively, such as population growth rates or interest rates of a financial investment.
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. The vertical dashed lines are asymptotes for the harmonic means. In mathematics, the three classical Pythagorean means are the arithmetic ...
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.
Another application of this theorem provides a geometrical proof of the AM–GM inequality in the case of two numbers. For the numbers p and q one constructs a half circle with diameter p + q. Now the altitude represents the geometric mean and the radius the arithmetic mean of the two numbers.
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 ).
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 series is an infinite series derived from a special type of sequence called a geometric progression.This means that it is the sum of infinitely many terms of geometric progression: starting from the initial term , and the next one being the initial term multiplied by a constant number known as the common ratio .
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 ...