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# Topic: Weighted harmonic mean

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 PlanetMath: arithmetic mean In the special case where all the weights are equal to each other, the weighted mean equals the arithmetic mean. See Also: geometric mean, harmonic mean, arithmetic-geometric-harmonic means inequality, general means inequality, weighted power mean, power mean, geometric distribution, root-mean-square, proof of general means inequality, proof of arithmetic-geometric-harmonic means inequality, derivation of geometric mean as the limit of the power mean, mean, a prime theorem of a convergent sequence This is version 8 of arithmetic mean, born on 2001-10-20, modified 2006-11-11. planetmath.org /encyclopedia/Mean.html   (181 words)

 Mean - Encyclopedia, History, Geography and Biography Sample mean is often used as an estimator of the central tendency such as the population mean. The mean is the unique value about which the sum of squared deviations is a minimum.If you calculate the sum of squared deviations from any other measure of central tendency, it will be larger than for the mean.This explains why the standard deviation and the mean are usually cited together in statistical reports. The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or most likely (mode). www.arikah.net /encyclopedia/Mean   (1120 words)

 Harmonic mean: Definition and Links by Encyclopedian.com ...Harmonic mean Harmonic mean In mathematics, the harmonic mean is one of...an average. In mathematics, the harmonic mean is one of several methods of calculating an average. The harmonic mean is never larger than the geometric mean or the arithmetic mean (see generalized mean). www.encyclopedian.com /ha/Harmonic-mean.html   (337 words)

 Arithmetic mean The mean may be conceived of as an estimate of the median. When the mean is not an accurate estimate of the median, the set of numbers, or frequency distribution, is said to be skewed. Note that several other "means" have been defined, including the generalized mean, the harmonic mean, the arithmetic-geometric mean, and the weighted mean. www.ebroadcast.com.au /lookup/encyclopedia/ar/Arithmetic_mean.html   (338 words)

 mean For example, the geometric mean of 3, 8, and 10 is (3 x 8 x 10)1/3 or the cube root of 240. The harmonic mean is the reciprocal of, or one over, the mean of the reciprocals of the values. If, in a set of observations, the observations are weighted according to their relative reliability, the individual values are first multiplied by weighting factors before they are summed and the mean taken; this is then called a weighted mean. www.daviddarling.info /encyclopedia/M/mean.html   (314 words)

 Mean - Psychology Wiki - a Wikia wiki The mean is the arithmetic average of a set of values, or distribution; however, for skewed distributions, the mean is not necessarily the same as the middle value (median), or most likely (mode). The geometric mean is an average that is useful for sets of numbers that are interpreted according to their product and not their sum (as is the case with the arithmetic mean). The harmonic mean is an average which is useful for sets of numbers which are defined in relation to some unit, for example speed (distance per unit of time). psychology.wikia.com /wiki/Mean   (1137 words)

 Weighted harmonic mean - Wikipedia, the free encyclopedia Note that if all the weights are equal, the weighted harmonic mean is the same as the harmonic mean. Probably the best known weighted mean is the weighted arithmetic mean, usually simply called the weighted mean. Another example of a weighted mean is the weighted geometric mean. en.wikipedia.org /wiki/Weighted_harmonic_mean   (96 words)

 Mean : search word Sample mean is often used as an estimator of the central tendency such as the population mean. The geometric mean is an average which is useful for sets of numbers which are interpreted according to their product and not their sum (as is the case with the arithmetic mean). The generalized mean is an abstraction of the Arithmetic, Geometric and Harmonic Means. www.searchword.org /me/mean.html   (1130 words)

 Mean   (Site not responding. Last check: 2007-09-17) The mean is the unique value about the sum of squared deviations is a If you calculate the sum of squared from any other measure of central tendency it will be larger than for mean. The harmonic mean is an average which is useful sets of numbers which are defined in to some unit for example speed (distance per unit of time). The generalized mean is an abstraction of the Arithmetic and Harmonic Means. www.freeglossary.com /MeaN   (957 words)

 Weighted Harmonic Average -- Recommendations and Resources The ''number average'' molecular weight is the common average of the molecular weights of the individual polymers. It is determined by measuring the molecular weight of ''n'' polymer molecules, summing the weights, and dividing by ''n''. An alternative measure of the molecular weight of a polymer is the weight average molecular weight. www.becomingapediatrician.com /health/170/weighted-harmonic-average.html   (876 words)

 Weighted mean - Wikipedia, the free encyclopedia If all the weights are equal, then the weighted mean is the same as the arithmetic mean. While weighted means generally behave in a similar fashion to arithmetic means, they do have a few counter-intuitive properties, as captured for instance in Simpson's paradox. Examples of such weighted means include the weighted geometric mean and the weighted harmonic mean. en.wikipedia.org /wiki/Weighted_mean   (413 words)

 The Super-Symmetric Mean The famous Arithmetic-Geometric Mean (AGM) has found many uses in analysis (e.g., elliptic integrals) and number theory (e.g., quadratically convergent algorithms for computing the digits of PI), but there does not seem to have been much attention devoted to higher-order versions of iterated means of more than two arguments. The Holder mean M_k() is defined by the above formula with f(x)=x^k, from which it follows that M_1() is the Arithmetic mean, M_-1() is the Harmonic mean, M_2() is the root-sum-square, and the limit of M_k() as k goes to infinity is the Geometric mean. However, these means are all just (in a sense) weighted version of a single prototype, and don't seem to capture the essence of the desired generalization of the AGM. www.mathpages.com /home/kmath461.htm   (768 words)

 PlanetMath: weighted power mean See Also: arithmetic-geometric-harmonic means inequality, arithmetic mean, geometric mean, harmonic mean, power mean, proof of arithmetic-geometric-harmonic means inequality, root-mean-square, proof of general means inequality, derivation of geometric mean as the limit of the power mean Cross-references: weights, power means inequality, limit, continuous function, power mean, real numbers, positive This is version 7 of weighted power mean, born on 2001-10-17, modified 2005-01-30. planetmath.org /encyclopedia/WeightedPowerMean.html   (120 words)

 Other descriptive statistics This is obtained by "weighting" the means by 30 and 50, respectively, and dividing by the sum of the wieghts. The harmonic mean is the reciprocal of the arithmetic mean of the reciprocals. For one of my classes, the mean weight was 152 pounds, with a standard deviation of 31 pounds; the mean height was 69.3 inches, with a standard deviation of 3.86 inches. www.cs.uni.edu /~campbell/stat/cba3.html   (677 words)

 Geometric Mean and Harmonic Mean Not to worry: the mean is the appropriate single-point forecast 95+% of evaluation uses. The harmonic mean is a better "average" when the numbers are defined in relation to some unit. In petroleum engineering, the harmonic mean is sometimes the better "average" for vertical permeability with horizontally-layered bedding. www.maxvalue.com /tip104.htm   (488 words)

 Math Forum - Ask Dr. Math Archives: Middle School Statistics Make up a set of 5 numbers with a mean of 20, a median of 10, and a range of 50. We are always talking about 'They range in age from, or they range in height, or they range in weight, or they range in size, etc'. I have some data on the weight of various parts of the human body. mathforum.org /library/drmath/sets/mid_statistics.html   (855 words)

 LIFO Glossary to calculate weighted average pool indexes whereby current year cost balances are "deflated" to prior year prices by division of the current year cost by the current year inflation index for that CPI or PPI index category to determine a Harmonic Mean "extension". The pool index is calculated by dividing sum of the current year cost by the sum of the Harmonic Mean extensions. Weighted Arithmetic Mean - A method for calculation of weighted average pool indexes whereby current year cost balances are multiplied times the current year inflation index for that CPI or PPI index category to determine an Arithmetic Mean "extension". www.lifopro.com /glossary.html   (1341 words)

 Harmonic mean - Wikipedia, the free encyclopedia   (Site not responding. Last check: 2007-09-17) Another formula for the harmonic mean of two numbers is to multiply the two numbers, and divide that quantity by the arithmetic mean of the two numbers. Since R is the harmonic mean of p and q, this means that the object and its image must lie on either side of the center of curvature: not both on the same side. It also means that both object and image lie beyond the focus (away from the vertex), i.e. www.godseye.com /stat/en/h/a/r/Harmonic_mean.html   (427 words)

 NERSC Projects: SSP - Sustained System Performance Compute Metric: Compute the weighted harmonic mean of kernel execution rates to normalize the "peak" performance of the system to a number that would likely be delivered in practice on the computing center's mix of applications. The weighted harmonic mean of timings presumes the applications are either serial (as was the case when the report was first written) or that they are run in parallel at same level of concurrency. The harmonic mean of wall clock times is probably appropriate in cases where the workload balance is expected to remain relatively static. web-dev.nersc.gov /projects/ssp.php   (3009 words)

 SPECviewperf® 7.1 -- Weighted Geometric Mean Above is the formula for determining a weighted geometric mean, where "n" is the number of individual tests in a viewset, and "w" is the weight of each individual test, expressed as a number between 0.0 and 1.0. Since the weights for the viewsets were selected on percentage of time, not percentage of operations, we chose the weighted geometric mean over the weighted harmonic mean. The weighted arithmetic mean is correct for calculating grades at the end of a school term. www.spec.org /gpc/opc.static/geometric.html   (757 words)

 Pythagorean means   (Site not responding. Last check: 2007-09-17) Pythagorean means is one of the topics in focus at Global Oneness. The harmonic mean is one of the Pythagorean means and is never larger than the geometric mean or the arithmetic mean (the other two Pythagorean means). When dealing with just two numbers, an equivalent, sometimes more convenient, formula of their harmonic mean is given by: In this case, their harmonic mean is related to their arithmetic mean, and their geometric mean, by... www.experiencefestival.com /pythagorean_means   (473 words)

 Cauchy boundary condition Summary It is sometimes said that Cauchy boundary conditions are a weighted average of imposing Dirichlet boundary conditions and Neumann boundary conditions. This should not be confused with statistical objects such as the weighted mean, the weighted geometric mean or the weighted harmonic mean, since no such formulas are used upon imposing Cauchy boundary conditions. Rather, the term weighted average means that while analyzing a given boundary value problem, one should bear in mind all available information for its well-posedness and subsequent successful solution. www.bookrags.com /Cauchy_boundary_condition   (883 words)

 Property Evidence The modified harmonic mean is continuous, gives additional weight to negative evidence and integrates all values uniformly. This means that we can add evidence incrementally without biasing the results to the earlier or later values (provided that we also keep track of the weighting of the values). This harmonic mean can be implemented in a value passing network, as shown in Figure 8.9, which integrates the evidence values homepages.inf.ed.ac.uk /rbf/BOOKS/FSTO/node41.html   (1013 words)

 Arithmetic Mean -- from Wolfram MathWorld The arithmetic mean of a set of values is the quantity commonly called "the" mean or the average. When viewed as an estimator for the mean of the underlying distribution (known as the population mean), the arithmetic mean of a sample is called the In this case, the variance of the sample mean is generally less than the variance of the sample median. mathworld.wolfram.com /ArithmeticMean.html   (345 words)

 Wikinfo | Mean The interquartile mean is used when a set of numbers (the data) might be contaminated by inaccurate (ie. This is simply the arithmetic mean after removing a certain number of the lowest and the highest values. Images, some of which are used under the doctrine of Fair use or used with permission, may not be available. www.wikinfo.org /wiki.php?title=Mean   (708 words)

 The Harmonic Mean Many courses offered by the School of Computer Science and Engineering use a harmonic mean formula to calculate students' final results given their exam and assignment marks. Such a harmonic mean formula is a way of ensuring that in order to pass the course, students must have performed reasonably well in both aspects of the course. For example, a lecturer might weight exam, mid-session quiz, and assignments as 50%, 20% and 30%, and then combine those marks using a harmonic mean formula. www.cse.unsw.edu.au /~teachadmin/info/harmonic3.html   (426 words)

 Michael Thomas Flanagan's Java Library: Class Stat Returns the sample weighted variance of the n variables in the array of double or float, x, with weights, w, that should be estimates of the standard deviations of the data values, x. Returns the sample weighted standard deviation of the variables in the array of double or float, x, with an array of weights, w, that should be estimates of the standard deviation of each measurement, x. The argument, mean, is the mean of the Poisson distribution. www.ee.ucl.ac.uk /~mflanaga/java/Stat.html   (4197 words)

 What Does He Mean? In lesson 3, we defined arithmetic mean as the one commonly used by statisticians and as the one usually intended when we just say mean. The geometric mean is typically first encountered in a proportion when the means are equal, as in 8/w=w/4. Frequency mean is the same as obtaining the arithmetic mean from a frequency table. www.andrews.edu /~calkins/math/webtexts/stat04.htm   (1178 words)

 RMP Lecture Notes The Average Molecular Weight of a mixture is computed from the molar composition and the molecular weight. It is a weighted average -- the molecular weights are averaged using the mole fractions as weights. You have to use a weighted harmonic mean. www.cbu.edu /~rprice/lectures/compos.html   (822 words)

 What the Weighted Geometric Mean Means for Viewperf In May 1995, the OPC project group decided to adopt a weighted geometric mean as the single composite metric for each viewset. Since the weights for the view sets were selected on percentage of time, not percentage of operations, we chose the weighted geometric mean over the weighted harmonic mean. Since our weights were percentage of time and since the results from Viewperf are expressed in frames/sec, we were not obligated to normalize. www.spec.org /gpc/Oct96/opc.static/geometric_mean.html   (639 words)

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