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In mathematics, the harmonic mean is a kind of average, one of the Pythagorean means. It is the most appropriate average for ratios and rates such as speeds, [1] [2] ...
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
Subcontrary, which we call harmonic, is the mean when they are such that, by whatever part of itself the first term exceeds the second, by that part of the third the middle term exceeds the third. It turns out that in this proportion the interval between the greater terms is greater and that between the lesser terms is less.
The weighted harmonic mean of p-values , …, is defined as = = = /, where , …, are weights that must sum to one, i.e. = =.Equal weights may be chosen, in which case = /.. In general, interpreting the HMP directly as a p-value is anti-conservative, meaning that the false positive rate is higher than expected.
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In mathematics, a harmonic progression (or harmonic sequence) is a progression formed by taking the reciprocals of an arithmetic progression, which is also known as an arithmetic sequence. Equivalently, a sequence is a harmonic progression when each term is the harmonic mean of the neighboring terms.
Harmonic number may also refer to: Harmonic, a periodic wave with a frequency that is an integral multiple of the frequency of another wave; Harmonic divisor numbers, also called Ore numbers or Ore's harmonic numbers, positive integers whose divisors have an integral harmonic mean; 3-smooth numbers, numbers whose only prime factors are 2 and 3
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