Inverse of the average of the inverses of a set of numbers
In mathematics, the harmonic mean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for situations when the average rate is desired.[1]
The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals of the given set of observations. As a simple example, the harmonic mean of 1, 4, and 4 is
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In mathematics, the harmonicmean is one of several kinds of average, and in particular, one of the Pythagorean means. It is sometimes appropriate for...
numbers. The geometric mean is one of the three classical Pythagorean means, together with the arithmetic mean and the harmonicmean. For all positive data...
Arithmetic-geometric mean Arithmetic-harmonicmean Cesàro mean Chisini mean Contraharmonic mean Elementary symmetric mean Geometric-harmonicmean Grand mean Heinz mean Heronian...
mathematics, a harmonic divisor number or Ore number is a positive integer whose divisors have a harmonicmean that is an integer. The first few harmonic divisor...
\dots } Harmonic numbers are related to the harmonicmean in that the n-th harmonic number is also n times the reciprocal of the harmonicmean of the first...
classical Pythagorean means are the arithmetic mean (AM), the geometric mean (GM), and the harmonicmean (HM). These means were studied with proportions...
sequence of harmonic functions is still harmonic. This is true because every continuous function satisfying the mean value property is harmonic. Consider...
In mathematics, the root mean square (abbrev. RMS, RMS or rms) of a set of numbers is the square root of the set's mean square. Given a set x i {\displaystyle...
F-measure (the weighted harmonicmean of precision and recall), or the Matthews correlation coefficient, which is a geometric mean of the chance-corrected...
a contraharmonic mean is a function complementary to the harmonicmean. The contraharmonic mean is a special case of the Lehmer mean, L p {\displaystyle...
{1}{n}}\cdot \sum {\frac {p_{0}}{p_{t}}}}}} Is the geometric mean of the Carli and the harmonic price indexes. In 1922 Fisher wrote that this and the Jevons...
for the i-th query. The reciprocal value of the mean reciprocal rank corresponds to the harmonicmean of the ranks. Suppose we have the following three...
The geometric mean (G) is G = x m exp ( 1 α ) . {\displaystyle G=x_{\text{m}}\exp \left({\frac {1}{\alpha }}\right).} The harmonicmean (H) is H = x...
_{p\to -\infty }M_{p}(x_{1},\dots ,x_{n})=\min\{x_{1},\dots ,x_{n}\}} harmonicmean M − 1 ( x 1 , … , x n ) = n 1 x 1 + ⋯ + 1 x n {\displaystyle M_{-1}(x_{1}...
exponent greater than 1. However, it is larger than the geometric mean and the harmonicmean, respectively. The inequalities are strict unless both numbers...
types of means, such as geometric and harmonic. In addition to mathematics and statistics, the arithmetic mean is frequently used in economics, anthropology...
In mechanics and physics, simple harmonic motion (sometimes abbreviated SHM) is a special type of periodic motion an object experiences due to a restoring...
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