Editing Harmonic mean (section)

=== In other sciences ===
In [[computer science]], specifically [[information retrieval]] and [[machine learning]], the harmonic mean of the [[Precision and recall|precision]] (true positives per predicted positive) and the [[Precision and recall|recall]] (true positives per real positive) is often used as an aggregated performance score for the evaluation of algorithms and systems: the [[F1 score|F-score]] (or F-measure). This is used in information retrieval because only the positive class is of [[relevance]], while number of negatives, in general, is large and unknown.<ref>{{cite book | last = Van Rijsbergen | first = C. J. | url = http://www.dcs.gla.ac.uk/Keith/Preface.html | year = 1979 | title = Information Retrieval | edition = 2nd | publisher = Butterworth | url-status = live | archive-url = https://web.archive.org/web/20050406090119/http://www.dcs.gla.ac.uk/Keith/Preface.html | archive-date = 2005-04-06 }}</ref> It is thus a trade-off as to whether the correct positive predictions should be measured in relation to the number of predicted positives or the number of real positives, so it is measured versus a putative number of positives that is an arithmetic mean of the two possible denominators.

A consequence arises from basic algebra in problems where people or systems work together. As an example, if a gas-powered pump can drain a pool in 4 hours and a battery-powered pump can drain the same pool in 6 hours, then it will take both pumps {{math|{{sfrac|6·4|6 + 4}}}}, which is equal to 2.4 hours, to drain the pool together. This is one-half of the harmonic mean of 6 and 4: {{math|{{sfrac|2·6·4|6 + 4}} {{=}} 4.8}}. That is, the appropriate average for the two types of pump is the harmonic mean, and with one pair of pumps (two pumps), it takes half this harmonic mean time, while with two pairs of pumps (four pumps) it would take a quarter of this harmonic mean time.

In [[hydrology]], the harmonic mean is similarly used to average [[hydraulic conductivity]] values for a flow that is perpendicular to layers (e.g., geologic or soil) - flow parallel to layers uses the arithmetic mean. This apparent difference in averaging is explained by the fact that hydrology uses conductivity, which is the inverse of resistivity.

In [[sabermetrics]], a baseball player's [[Power–speed number]] is the harmonic mean of their [[home run]] and [[stolen base]] totals.

In [[population genetics]], the harmonic mean is used when calculating the effects of fluctuations in the census population size on the effective population size. The harmonic mean takes into account the fact that events such as population [[wikt: bottlenecks|bottleneck]] increase the rate genetic drift and reduce the amount of genetic variation in the population.  This is a result of the fact that following a bottleneck very few individuals contribute to the [[gene pool]] limiting the genetic variation present in the population for many generations to come.

When considering [[fuel economy in automobiles]] two measures are commonly used – miles per gallon (mpg), and litres per 100&nbsp;km. As the dimensions of these quantities are the inverse of each other (one is distance per volume, the other volume per distance) when taking the mean value of the fuel economy of a range of cars one measure will produce the harmonic mean of the other – i.e., converting the mean value of fuel economy expressed in litres per 100&nbsp;km to miles per gallon will produce the harmonic mean of the fuel economy expressed in miles per gallon. For calculating the average fuel consumption of a fleet of vehicles from the individual fuel consumptions, the harmonic mean should be used if the fleet uses miles per gallon, whereas the arithmetic mean should be used if the fleet uses litres per 100&nbsp;km. In the USA the [[CAFE standards]] (the federal automobile fuel consumption standards) make use of the harmonic mean.

In [[chemistry]] and [[nuclear physics]] the average mass per particle of a mixture consisting of different species (e.g., molecules or isotopes) is given by the harmonic mean of the individual species' masses weighted by their respective mass fraction.