About the statistical concept In statistics , mean has two related meanings the arithmetic mean and is distinguished from the geometric mean or harmonic mean . the expected value of a random variable , which is also called the population mean . There are other statistical measures that should not be confused ... . For a real valued random variable X , the mean is the expectation operator expectation of X . Note that not every probability distribution has a defined mean or variance see the Cauchy distribution for an example. For a data set , the mean is the sum of the values divided by the number of values. The mean of a set of numbers x sub 1 sub , x sub 2 sub , ..., x sub n sub is typically denoted by math bar x math , pronounced x bar . This mean is a type of arithmetic mean. If the data set were based on a series of observations obtained by sampling statistics sampling a statistical population , this mean is termed the sample mean math bar x math to distinguish it from the population mean math mu math or math mu math sub x sub . The mean is often quoted along with the standard deviation the mean ... measure of dispersion is the mean deviation, equivalent to the average absolute deviation from the mean. It is less sensitive to outliers, but less mathematically tractable. If a series of observations ... to construct a population mean , which is also the expected value for a sample drawn from this population ... mean of the given property for every member of the population. For a probability distribution, this would ... convention to represent the population mean by the symbol math mu math . ref Underhill ... distribution , the mean of a discrete random variable x is given by taking the product of each ... books?id DWCAh7jWO98C&lpg PP1&pg PA279 v onepage&q&f false p. 279 ref The sample mean may differ from the population mean, especially for small samples, but the law of large numbers dictates that the larger the size of the sample, the more likely it is that the sample mean will be close ... more details
wiktionary meanMean is a term used in math and statistics. Mean may also refer to Mean song Mean song , a 2010 country song by Taylor Swift from Speak Now Mean album Mean album , an album by Montrose Mean magazine , an American bi monthly magazine Mean, an archaic male choral vocal range approximating mezzo soprano Ethic mean , a sociology term See also Means disambiguation disambiguation fa nl Mean ... more details
Mr. Mean may refer to Mr. Mean album Mr. Mean album , a 1977 album by The Ohio Players Mr. Mean Mr. Men Mr. Mean Mr. Men , a character and book from the Mr. Men book series disambiguation ... more details
Mean Machine may refer to Music Mean Machine Lucifer s Friend album Mean Machine Lucifer s Friend album Mean Machine U.D.O. album Mean Machine U.D.O. album Mean Machine band , a Japanese rock band The Mean Machine rap group Mean Machine, a song by Mot rhead on the album Orgasmatron album Orgasmatron Mean Machine, a song by Sugar Ray on the album Lemonade and Brownies Sport Mean Machine Sailing Team Roy Shaw , British boxer Mean Machine RFC , a rugby club in the Kenya Rugby Football Union Football teams in the 1974 film The Longest Yard 1974 film The Longest Yard and The Longest Yard 2005 film its 2005 remake A 1982 Commonwealth Games relay team including Graeme Brewer , Neil Brooks , Greg Fasala , and Michael Delany Other uses Mean Machine film Mean Machine film Mean Machine Angel , a character in the Judge Dredd universe Mean Machine, a List of Hi Hi Puffy AmiYumi episodes Hi Hi Puffy AmiYumi episode The Mean Machine, Dick Dastardly s car in the TV series Wacky Races disambig pt Mean Machine ... more details
The Mean Reds can mean either one of these things The rock band, The Mean Reds band The Mean Reds . In the novella Breakfast at Tiffany s novella Breakfast at Tiffany s by Truman Capote , Holly Golightly called her bouts of angst anxiety the mean reds. In the film, she described the mean reds as a feeling of being afraid, yet not knowing what you are afraid of. blockquote Holly Golightly You know those days when you get the mean reds? br Paul Varjak The mean reds. You mean like the blues? br Holly Golightly No. The blues are because you re getting fat, and maybe it s been raining too long. You re just sad, that s all. The mean reds are horrible. Suddenly you re afraid, and you don t know what you re afraid of. Do you ever get that feeling? blockquote disambig ... more details
In mathematics, a contraharmonic mean is a function complementary to the harmonic mean . The contraharmonic mean is a special case of the Lehmer mean , math L p math , where p 2. Definition The contraharmonic mean of a set of positive numbers is defined as the arithmetic mean of the squares of the numbers divided by the arithmetic mean of the numbers math C x 1, x 2, dots , x n left x 1 2 x 2 2 cdots ... the characteristic properties of a mean math C x 1, x 2, dots , x n in min x 1, x ... k fixed point property . The contraharmonic mean is higher in value than the average and also higher than the root mean square math min mathbf x leq H mathbf x leq G mathbf x leq L mathbf x leq ... mean, G is geometric mean , L is the logarithmic mean , A is the arithmetic mean, R is the root mean square and C is the contraharmonic mean. Unless all values of x are the same, the math le ... taking the mean of only two variables, the contraharmonic mean is as high above the arithmetic mean as the arithmetic mean is above the harmonic mean i.e., the arithmetic mean of the two variables is equal to the arithmetic mean of their harmonic and contraharmonic means . Two variable formulae From the formulas for the arithmetic mean and harmonic mean of two variables we have math A a,b a b ... mean A H a , b , C a , b A a , b As a gets closer to 0 then H a , b also gets closer to 0. The harmonic mean is very sensitive to low values. On the other hand, the contraharmonic mean is sensitive to larger values, so as a approaches 0 then C a , b approaches ... 2 variable means. First, the geometric mean of the arithmetic and harmonic means is equal to the geometric mean of the two values math G A a,b , H a,b G left a b over 2 , 2ab over a b right sqrt a b over 2 cdot 2ab over a b sqrt ab G a,b math The second relationship is that the geometric mean of the arithmetic and contraharmonic means is the root mean square math G A a,b , C a,b G left a b over 2 ... more details
wiktionary golden mean Golden mean may refer to Doctrine of the Golden Mean Chinese pinyin Zh ng Y ng , a chapter in Li Ji , one of the Four Books of Confucianism Golden mean philosophy , the felicitous middle between the extremes of excess and deficiency Golden ratio , a specific mathematical ratio sometimes called golden mean The Golden Mean novel , the third novel in Nick Bantock s series, The Griffin and Sabine Trilogy The golden mean fallacy, another name for the argument to moderation See also Ethic of reciprocity , also known as the Golden Rule disambiguation pl Z oty rodek ... more details
Mean to Me can refer to Song titles Mean to Me 1929 song Mean to Me 1929 song , a 1929 song with music by Fred E. Ahlert and lyrics by Roy Turk . Mean to Me Crowded House song Mean to Me Crowded House song , a 1986 song by Crowded House , from their Crowded House album self titled debut album . Mean to Me , a 1999 song from the Sugar Tonic album Sugar album by Tonic band Tonic . Mean to Me , a 2012 song by Ben Kweller , from his album Go Fly a Kite . disambig ... more details
Mean reversion may refer to See Regression toward the mean Ornstein&ndash Uhlenbeck process Mean reversion finance disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
Unreferenced date January 2010 Context date October 2010 The Fr chet mean named after Maurice Fr chet , is the point, x , that minimizes the Fr chet function, in cases where such a unique minimizer exists. The value at a point p , of the Fr chet function associated to a random point X on a complete metric space M , d is the expected squared distance from p to X . In particular, the Fr chet mean of a set of discrete random points x sub i sub is the minimizer m of the weighted sum of squared distances ... mean is sometimes used instead of Fr chet mean , where this refers to Hermann Karcher. Citation needed date October 2010 Examples of Fr chet Means Arithmetic mean For real numbers, the arithmetic mean is a Fr chet mean, using as distance function the usual Euclidean distance. Citation needed date October 2010 Geometric mean On the positive real numbers, the hyperbolic distance function math d x,y log x log y math can be defined. The geometric mean is the corresponding Fr chet mean.Indeed math ... respect the Fr chet mean the Fr chet mean of the math x i math is the image by math f math of the Fr chet mean in the euclidean sense of the math f 1 x i math , i.e. it must be math f frac 1 n sum i 1 n f 1 x i exp frac 1 n sum i 1 n log x i sqrt n x 1 cdots x n math . Harmonic mean On the positive ... math can be defined. The harmonic mean is the corresponding Fr chet mean. Citation needed date October 2010 Power means Given a non zero real number math m math , the power mean can be obtained as a Fr chet mean by introducing the metric Citation needed date October 2010 math d m x,y x m y m math . f mean Given an invertible function math f math , the f mean can be defined as the Fr chet mean ... called the Generalised f mean or Quasi arithmetic mean . Weighted means The general definition of the Fr chet mean that includes the possibility of weighting observations can be used to derive weighted versions for all of the above types of means. Notes Reflist DEFAULTSORT Frechet Mean Category ... more details
Refimprove date July 2010 A truncated mean or trimmed mean is a Statistics statistical Average measure of central tendency , much like the mean and median . It involves the calculation of the mean after ... mean , but this name should not be confused with the Winsorized mean in the latter, the observations that the trimmed mean would discard are instead replaced by the largest smallest of the remaining values. Notation The index of the mean is an indication of the percentage of the entries removed on both ... the first and the last entry in the sample when calculating the truncated mean. Interpolation When a trimmed mean for a sample must be determined, but it cannot be accurately done, the best is to calculate ... the 15 trimmed mean of a sample containing 10 entries, you would calculate the 10 trimmed mean removing 1 entry on either side of the sample , the 20 trimmed mean removing 2 entries on either side , and interpolating to determine the 15 trimmed mean. Advantages The truncated mean is a useful estimator because it is less sensitive to outlier s than the mean but will still give a reasonable estimate of central tendency or mean for many statistical models. In this regard it is referred ... mean is when estimating the location parameter of a Cauchy distribution , a bell shaped probability ... mean of the middle 24 sample order statistics i.e., truncate the sample by 38 produces an estimate ... or the full sample mean. ref name rothenberg cite journal last1 Rothenberg first1 Thomas J. last2 Fisher ... mean, full sample mean or sample median represents a maximum likelihood estimator, nor are any as asymptotically ... is difficult to compute, leaving the truncated mean as a useful alternative. ref name bloch ref name ... mean uses more information from the distribution or Sample statistics sample than the median , but unless the underlying distribution is Symmetry symmetric , the truncated mean of a sample is unlikely to produce an Bias of an estimator unbiased estimator for either the mean or the median. Examples ... more details
In mathematics , a function f of n variables x sub 1 sub , ..., x sub n sub leads to a Chisini mean M if for every vector < x sub 1 sub ... x sub n sub > , there exists a unique M such that f M , M , ..., M f x sub 1 sub , x sub 2 sub , ..., x sub n sub . The arithmetic mean arithmetic , harmonic mean harmonic , geometric mean geometric , generalised mean generalised , Heronian mean Heronian and quadratic mean quadratic means are all Chisini means, as are their weighted variants. References They were introduced by Oscar Chisini , in the paper Chisini, O. Sul concetto di media. Periodico di Matematiche 4, 106&ndash 116, 1929. Category Mathematical analysis Category Means it Media Chisini pl rednia Chisinego ... more details
In astrodynamics and celestial mechanics , mean longitude is the longitude at which an orbiting body could be found if its orbit were circular orbit circular , and free of perturbation astronomy perturbations , and if its inclination were zero. Description Both the mean longitude and the true longitude of the body in the orbit described above would change at a constant rate over time. ref name Moulton 1970 Multon, F. R. 1970 . An Introduction to Celestial Mechanics , 2nd ed., p. 182&ndash 183. New York, NY Dover. ref ref name Roy 1978 Roy, A. E. 1978 . Orbital Motion , p. 174, ISBN 0 470 99251 4 . New York, NY John Wiley & Sons. ref ref name Brouwer Clemence 1961 Brouwer, D., & Clemence ... not change at a constant rate over time. So the mean longitude is an abstracted quantity for Keplerian ... body the difference between the mean longitude and the true longitude is usually called the equation of the center . In such an elliptical orbit, the only times when the mean longitude is equal ... orbit. For each successive set of osculating elements, a mean longitude can be defined, as in the unperturbed case. But here, the changes in mean longitude over time will not only be those due to some ... perturbed . A set of mean elements can still be defined for such an orbit, after abstracting the perturbational variations with time. The term mean longitude was already used for the unperturbed and osculating cases, and the corresponding mean longitude member in a set of mean elements, after abstraction of the periodic variations, is sometimes therefore called the meanmean longitude . To arrive at a true longitude from a meanmean longitude, the perturbational terms must be applied as well as the equation of the center. Calculation The mean longitude math L , math can be calculated as follows ref name Roy 1978 math L M varpi M Omega omega , math where math M , math is orbit s mean ... of periapsis . References references Orbits DEFAULTSORT Mean Longitude Category Astrodynamics ... more details
In mathematics, the Heronian mean H of two non negative real number s A and B is given by the formula math H frac 1 3 left A sqrt A B B right . math It is named after Hero of Alexandria , and used in finding the volume of a frustum of a pyramid or cone geometry cone . The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces. The Heronian mean of the numbers A and B is a weighted mean of their arithmetic mean arithmetic and geometric mean s math H frac 2 3 cdot frac A B 2 frac 1 3 cdot sqrt A B . math References Citation last1 Bullen first1 P.S. title Handbook of Means and Their Inequalities publisher Springer Science Business Media location Berlin, New York edition 2nd series Mathematics and Its Applications isbn 978 1 4020 1522 9 year 2003 Citation last1 Eves first1 Howard Whitley author1 link Howard Eves title Great Moments in Mathematics Before 1650 publisher Mathematical Association of America isbn 978 0 88385 310 8 year 1980 External links http jwilson.coe.uga.edu EMT668 EMAT6680.2000 Umberger EMAT6690smu Essay3smu Essay3smu.html Mean Trapezoids Geometric comparison of some mathematical means DEFAULTSORT Heronian Mean Category Means geometry stub es Media heroniana eu Batezbesteko herondar ko km zh ... more details
Refimprove date January 2010 The identric mean of two positive real number s x , y is defined as math begin align I x,y & frac 1 e cdot lim xi, eta to x,y sqrt xi eta frac xi xi eta eta 8pt & lim xi, eta to x,y exp left frac xi cdot ln xi eta cdot ln eta xi eta 1 right 8pt & begin cases x & text if x y 8pt frac 1 e sqrt x y frac x x y y & text else end cases end align math It can be derived from the mean value theorem by considering the secant of the graph of the function math x mapsto x cdot ln x math . It can be generalized to more variables according by the mean value theorem for divided differences . The identric mean is a special case of the Stolarsky mean . See also Mean References MathWorld title Identric Mean urlname IdentricMean DEFAULTSORT Identric Mean Category Means km ... more details
The grand mean is the mean of the means of several subsamples. ref Everitt,2002 ref For example, consider several lots, each containing several items. The items from each lot are sampling statistics sampled for a Measurement measure of some variable and the means of the measurements from each lot are computed. The mean of the measures from each lot constitute the subsample mean. The mean of these subsample means is then the grand mean. Example Bob is interested in determining which American states have the tallest people. To do so Bob measures the height of a suitably sized sample of individuals in each state, separating individuals into groups by gender. Next Bob calculates the respective means for each state, and finally the grand mean for each gender with the corresponding standard deviation . Now Bob has the necessary information for a preliminary determination of which states have abnormally tall or short individuals by comparing the means of each state to the grand mean the standard deviation. Notes references References Everitt, B.S. 2002 Cambridge Dictionary of Statistics 2nd Edition , CUP. ISBN 052181099x Category Statistical terminology Category Data analysis es Gran media ... more details
Refimprove date September 2009 A Winsorized mean is a Winsorising Winsorized statistical measure of central tendency , much like the mean and median , and even more similar to the truncated mean . It involves the calculation of the mean after replacing given parts of a probability distribution or Sampling statistics sample at the high and low end with the most extreme remaining values, ref Yadolah Dodge Dodge, Y 2003 The Oxford Dictionary of Statistical Terms , OUP. ISBN 0 19 920613 9 entry for Winsorized estimation ref typically doing so for an equal amount of both extremes often 10 to 25 percent of the ends are replaced. Advantages The Winsorized mean is a useful estimator because it is less sensitive to outlier s than the mean but will still give a reasonable estimate of central tendency or mean for almost all statistical models. In this regard it is referred to as a robust estimator . Drawbacks The Winsorized mean uses more information from the distribution or sample than the median . However, unless the underlying distribution is symmetric , the truncated mean of a sample is unlikely to produce an unbiased estimator for either the mean or the median. Example For a sample of 10 numbers from x sub 1 sub , the smallest, to x sub 10 sub the largest the 10 Winsorized mean is math frac overbrace x 2 x 2 x 3 x 4 x 5 x 6 x 7 x 8 overbrace x 9 x 9 10 . , math The key is in the repetition of x sub 2 sub and x sub 9 sub the extras substitute for the original values x sub 1 sub and x sub 10 sub which have been discarded and replaced. Notes reflist inline date March 2012 References citation first1 R.R. last1 Wilcox first2 H.J. last2 Keselman title Modern robust data analysis methods Measures of central tendency year 2003 journal Psychological Methods volume 8 pages 254 274 pmid 14596490 issue 3 doi 10.1037 1082 989X.8.3.254 Category Means Category Robust statistics eu Winsortarturiko batezbesteko nl Winsorgemiddelde pl rednia winsorowska ... more details
Orphan date September 2008 Infobox magazine title Mean logo logo size image file Mean magazine September October 2005 cover.jpg image size image alt image caption September October 2005 cover editor editor title previous editor staff writer photographer category frequency Bi monthly circulation publisher Kashy Khaledi Media founder founded firstdate Start date year month day company country based language website URL meanmag.net issn oclc MEAN Music, Entertainment, Art News is an American bi monthly magazine that covers a wide spectrum of pop culture, focusing on trailblazers in the fields of fashion , art , and Film cinema . It began as a popular music zine in 1997 and continued in that format through 2001, before being re launched as a national lifestyle publication in 2004. Mean is published by Kashy Khaledi Media and distributed by Curtis Circulation Maxim magazine Maxim , TV Guide . Mainly appealing to urban trendsetters between the ages of 21 and 46, Mean has featured a broad assortment of personalities on its cover. Recent covers have included Adrien Brody , Emily Blunt , Samuel L. Jackson and Christina Ricci , Emile Hirsch , Javier Bardem , and Ewan McGregor portraying Woody Allen . External links http meanmag.net Mean Magazine Online cite press release title Kashy Khaledi Extends Mean Streak... His Mean Magazine Launches Vol. 2 publisher P.R. News Wire date 2004 02 23 format language url http www.prnewswire.com cgi bin stories.pl?ACCT 104&STORY www story 02 23 2004 0002114926&EDATE accessdate 2008 01 10 quote http dwb.sacbee.com content lifestyle story 10257344p 11177641c.html Sacramento Bee Getting Mean http findarticles.com p articles mi m5072 is 14 26 ai 115347048 L.A. Business Journal Deeper Mean ing http popsugar.com 814213 PopSugar.com Javier Bardem on No Country For Old Men in Mean Magazine http www.curtiscirc.com Curtis Circulation Category Fashion magazines Category American magazines Category Bi monthly magazines Category Magazines established in 1997 ... more details
In mathematics , the harmonic mean sometimes called the subcontrary mean is one of several kinds of average .... The harmonic mean H of the positive real number s x sub 1 sub , x sub 2 sub , ..., ... the third formula in the above equation it is more apparent that the harmonic mean is related to the arithmetic mean and geometric mean . Equivalently, the harmonic mean is the Multiplicative inverse reciprocal of the arithmetic mean of the reciprocals. As a simple example, the harmonic mean of 1 ... of the three Pythagorean means of two numbers, a and b . Harmonic mean is denoted by H in purple color. The Q denotes a fourth mean, the quadratic mean . The harmonic mean is one of the three ... mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between. If all values in a nonempty dataset ... mean . Since the harmonic mean of a list of numbers tends strongly toward the least elements of the list, it tends compared to the arithmetic mean to mitigate the impact of large outliers and aggravate the impact of small ones. The arithmetic mean is often mistakenly used in places calling for the harmonic mean. ref Statistical Analysis , Ya lun Chou, Holt International, 1969, ISBN 0030730953 ref In the speed example Examples below for instance the arithmetic mean 50 is incorrect, and too big. The harmonic mean is related to the other Pythagorean means, as seen in the third formula in the above equation. This is noticed if we interpret the denominator to be the arithmetic mean of the product ... on. The numerator, excluding the n , which 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. If a set of non identical numbers is subjected to a mean preserving spread that is, two or more elements of the set are spread apart from each other while leaving the arithmetic mean unchanged then the harmonic ... more details
More footnotes date May 2010 In mathematics and statistics , the arithmetic mean , or simply the mean ... of an Experiment probability theory experiment . The term arithmetic mean is preferred in mathematics and statistics because it helps distinguish it from other average mean s such as the geometric mean geometric and harmonic mean . In addition to mathematics and statistics, the arithmetic mean is used ... average income of a nation s population. While the arithmetic mean is often used to report central ... by outlier s. Notably, for skewed distribution s, the arithmetic mean may not accord with one s notion .... Definition Suppose we have sample space math a 1, ldots,a n math . Then the arithmetic mean ... population , then the mean of that population is called a population mean . If the list is a sampling statistics statistical sample , we call the resulting statistic a sample mean . The arithmetic mean of a variable is often denoted by a bar, for example math bar x math read x bar would be the mean of some sample space math X math . Motivating properties The arithmetic mean has several properties ... x 1, ldots,x n math have mean X, then math x 1 X ldots x n X 0 math . Since math x i X math is the distance from a given number to the mean, one way to interpret this property is as saying that the numbers to the left of the mean are balanced by the numbers to the right of the mean. The mean is the only ... mean does this best, in the sense of minimizing the sum of squares x sub i sub &minus X sup 2 sup of the errors and residuals in statistics residuals . It follows that the mean is also the best single predictor in the sense of having the lowest root mean squared error . For a normal distribution , the arithmetic mean is equal to both the median and the mode, other measures of central tendency. Problems Image Comparison mean median mode.svg thumb 300px Comparison of mean , median ... mean may be misinterpreted as the median to imply that most values are higher or lower than is actually ... more details
In celestial mechanics , the mean anomaly is a parameter relating position and time for a body moving in a Kepler orbit . It is based on the fact that equal areas are swept at the focus in equal intervals of time. The mean anomaly increases uniformly from 0 to math 2 pi math radians during each orbit. However, it is not an angle. Due to Kepler laws Kepler s second law , the mean anomaly is proportional to the area swept by the focus geometry focus to body line since the last periapsis . The mean anomaly is usually denoted by the letter math M math , and is given by the formula math M n , t sqrt frac G M star m a 3 ,t math where n is the mean motion , a is the length of the orbit s semi major axis , math M star math and m are the orbiting masses, and G is the gravitational constant . The mean anomaly is the time since the last periapsis multiplied by the mean motion , and the mean motion is math 2 pi math divided by the orbital period duration of a full orbit . The mean anomaly is one of three angular parameters anomalies that define a position along an orbit the other two being the eccentric anomaly and the true anomaly . If the mean anomaly is known at any given instant, it can be calculated at any later or prior instant by simply adding or subtracting math sqrt frac G M star m a 3 , delta t math where math delta t math represents the time difference. The other anomalies can hence be calculated. Formulas The mean anomaly M can be computed from the eccentric anomaly E and the Eccentricity mathematics eccentricity e with Kepler s Equation math M E e cdot sin E math To find the position of the object in an elliptic Kepler orbit at a given time t , the mean anomaly is found by multiplying the time and the mean motion, then it is used to find the eccentric anomaly by solving Kepler s equation. It is also frequently seen math M M 0 nt math , Again n is the mean motion. However ... of M sub 0 sub was taken. The value M sub 0 sub denotes the mean anomaly at epoch , which is the mean ... more details
In mathematics , the Stolarsky mean of two positive real number s x , y is defined as math begin align S p x,y & lim xi, eta to x,y left frac xi p eta p p xi eta right 1 p 1 10pt & begin cases x & text if x y left frac x p y p p x y right 1 p 1 & text else end cases end align math It is derived from the mean value theorem , which states that a secant line , cutting the graph of a differentiable function math f math at math x, f x math and math y, f y math , has the same slope as a line tangent to the graph at some point math xi math in the Interval mathematics interval math x,y math . math exists xi in x,y f xi frac f x f y x y math The Stolarsky mean is obtained by math xi f 1 left frac f x f y x y right math when choosing math f x x p math . Special cases math lim p to infty S p x,y math is the minimum . math S 1 x,y math is the geometric mean . math lim p to 0 S p x,y math is the logarithmic mean . It can be obtained from the mean value theorem by choosing math f x ln x math . math S frac 1 2 x,y math is the power mean with exponent math frac 1 2 math . math lim p to 1 S p x,y math is the identric mean . It can be obtained from the mean value theorem by choosing math f x x cdot ln x math . math S 2 x,y math is the arithmetic mean . math S 3 x,y QM x,y,GM x,y math is a connection to the quadratic mean and the geometric mean . math lim p to infty S p x,y math is the maximum . Generalizations You can generalize the mean to n 1 variables by considering the mean value theorem for divided differences for the n th derivative . You obtain math S p x 0, dots,x n f n 1 n cdot f x 0, dots,x n math for math f x x p math . See also mean References Stolarsky, Kenneth B. http links.jstor.org sici?sici 0025 570X 28197503 2948 3A2 3C87 3AGOTLM 3E2.0.CO 3B2 6 Generalizations of the logarithmic mean , Mathematics Magazine , volume 48, number 2, March, 1975, pages 87&ndash 92 Category Means de Stolarsky Mittel km pl rednia Stolarskiego ... more details
In fluid dynamics , the fluid flow is often decomposed into a mean flow and deviation statistics deviation s from the mean . The averaging can be done either in space or in time, or by ensemble average ensemble averaging . Example Calculation of the mean flow may often be as simple as the mathematical mean simply add up the given flow rates and then divide the final figure by the number of initial readings. For example, given two Discharge hydrology discharges Q of 3 m s and 5 m s, we can use these flow rates Q to calculate the mean flow rate Q sub mean sub . Which in this case is Q sub mean sub 4 m s. References Citation title Wave interactions and fluid flows first Alex D. D. last Craik publisher Cambridge University Press year 1988 isbn 0 521 36829 4 Citation title A first course in turbulence first1 Hendrik last1 Tennekes author1 link Hendrik Tennekes first2 John L. last2 Lumley author2 link John L. Lumley publisher MIT Press year 1972 isbn 0 262 20019 8 fluiddynamics stub Category Fluid dynamics ... more details
The geometric mean , in mathematics , is a type of mean or average , which indicates the central tendency or typical value of a set of numbers. A geometric mean is often used when comparing different items ... 2012 ref . For example, the geometric mean can give a meaningful average to compare two companies ... for their financial viability. If an arithmetic mean was used instead of a geometric mean, the financial ... mean than a large percentage change in environmental sustainability e.g. going from 2 to 5 . The use of a geometric mean normalizes the ranges being averaged, so that no range dominates the weighting, and a given percentage change in any of the properties has the same effect on the geometric mean. So, a 20 change in environmental sustainability from 4 to 4.8 has the same effect on the geometric mean as a 20 change in financial viability from 60 to 72. The geometric mean is similar to the arithmetic mean , except that the numbers are multiplied and then the Nth root n th root where n is the count ... mean of two numbers, say 2 and 8, is just the square root of their product that is math radic 2 × 8 2 4 . As another example, the geometric mean of the three numbers 4, 1, and 1 32 is the cube ..., if the numbers are math x 1, ldots,x n math , the geometric mean math G math satisfies math ... expression states that the log of the geometric mean is the arithmetic mean of the logs of the numbers. The geometric mean can also be understood in terms of geometry . The geometric mean of two numbers ... of a rectangle with sides of lengths a and b . Similarly, the geometric mean of three numbers, a , b ... whose lengths are equal to the three given numbers. The geometric mean applies only to positive numbers. ref The geometric mean only applies to positive numbers in order to avoid taking the root of a negative ... allows 0 which yields a geometric mean of 0 , but may be excluded, as one frequently wishes to take ... human population or interest rates of a financial investment. The geometric mean is also one of the three ... more details
Encyclopedia
top
