In mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite collection of positive real numbers by using the...

the inequality of arithmetic and geometric means, or more briefly the AM–GM inequality, states that the arithmetic mean of a list of non-negative real numbers...

mathematics, the geometric–harmonic mean M(x, y) of two positive real numbers x and y is defined as follows: we form the geometric mean of g0 = x and h0...

arithmetic–geometric mean (AGM or agM) of two positive real numbers x and y is the mutual limit of a sequence of arithmetic means and a sequence of geometric means...

In Euclidean geometry, the right triangle altitude theorem or geometric mean theorem is a relation between the altitude on the hypotenuse in a right triangle...

In statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. Given a sample x = ( x 1 , x...

Arithmetic-geometric mean Arithmetic-harmonic mean Cesàro mean Chisini mean Contraharmonic mean Elementary symmetric mean Geometric-harmonic mean Grand mean Heinz...

The geometric mean filter is an image filtering process meant to smooth and reduce noise of an image. It is based on the mathematic geometric mean. The...

converges to the sum of ⁠ 1 {\displaystyle 1} ⁠. Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same...

statistics, the geometric standard deviation (GSD) describes how spread out are a set of numbers whose preferred average is the geometric mean. For such data...

arithmetic and geometric means that the geometric mean is lower than the mean. Similarly, the harmonic mean is lower than the geometric mean. The accompanying...

_{i=1}^{n}x_{i}^{p}\right)^{{1}/{p}}.} (See p-norm). For p = 0 we set it equal to the geometric mean (which is the limit of means with exponents approaching zero, as proved...

goes with the arithmetic mean, is the geometric mean to the power n. Thus the n-th harmonic mean is related to the n-th geometric and arithmetic means. The...

"arithmetic mean" is preferred in some mathematics and statistics contexts because it helps distinguish it from other types of means, such as geometric and harmonic...

converges to the sum of ⁠ 1 {\displaystyle 1} ⁠. Each term in a geometric series is the geometric mean of the term before it and the term after it, in the same...

exponent greater than 1. However, it is larger than the geometric mean and the harmonic mean, respectively. The inequalities are strict unless both numbers...

length of its radius is the arithmetic mean of a and b (since the radius is half of the diameter). The geometric mean can be found by dividing the diameter...

Hermann Karcher. On the real numbers, the arithmetic mean, median, geometric mean, and harmonic mean can all be interpreted as Fréchet means for different...

of arithmetic and geometric means. For any real vector a = ( a 1 , … , a n ) {\displaystyle a=(a_{1},\dots ,a_{n})} define the "a-mean" [a] of positive...

mean inequality chain, state the relationship between the harmonic mean, geometric mean, arithmetic mean, and quadratic mean (also known as root mean...

as the arithmetic mean and the geometric mean, using a function f {\displaystyle f} . It is also called Kolmogorov mean after Soviet mathematician Andrey...

classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonic mean (HM). These means were studied with proportions...

replaces two numbers by their arithmetic and geometric mean, in order to approximate their arithmetic-geometric mean. The version presented below is also known...

time since "1900, Jan. 0, Greenwich Mean noon", measured in Julian centuries of 36,525 days. The Sun's geometric mean longitude, freed from aberration is...

rectified value (ARV) Central moment Geometric mean L2 norm Least squares Glossary of mathematical symbols Mean squared displacement True RMS converter...

measure of central tendency, such as the mid-range, median, mode or geometric mean. For example, the average personal income is often given as the median –...

also leads to predictions which can be interpreted in terms of the geometric mean. People often think the MAPE will be optimized at the median. But for...

a square with the side x = a b {\displaystyle x={\sqrt {ab}}} (the geometric mean of a and b). For this purpose it is possible to use the following: if...

the covariance is negative. The magnitude of the covariance is the geometric mean of the variances that are in common for the two random variables. The...

cutoff frequencies. It is usually defined as either the arithmetic mean or the geometric mean of the lower cutoff frequency and the upper cutoff frequency of...