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Topic: Weighted mean

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Weighted harmonic mean

Weighted geometric mean

Weighted average

Generalized mean

Geometric mean

Inequality of arithmetic and geometric means

Arithmetic mean

Harmonic mean

Arithmetic geometric mean

Standard deviation

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	PlanetMath: arithmetic mean (Site not responding. Last check: 2007-09-10)
		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)

	Weighted mean - Wikipedia, the free encyclopedia
		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.
		The significance of this choice is that this weighted mean is the maximum likelihood estimator of the mean of the probability distributions under the assumption that they are independent and normally distributed with the same mean.
	en.wikipedia.org /wiki/Weighted_mean (530 words)

	Summary Statistics
		Mean annual yield was estimated by dividing the mean annual load by the upstream drainage-basin area.
		Mean annual load was then calculated as the product of the flow-weighted mean, the total streamflow for the estimation period, and an appropriate units-conversion factor.
		Mean annual yield was estimated by dividing the load by the upstream drainage-basin area.
	pubs.usgs.gov /ds/2005/152/htdocs/data_report_sum_stat.htm (504 words)

	GLM: Unequal n Designs (SPSS 8.0) (Site not responding. Last check: 2007-09-10)
		The weighted mean is found by weighting each of the cell means by its respective n (i.e., multiply each cell mean by its n) and then dividing by the total n for that marginal mean.
		That is, the weighted means are identical to means found by finding the sum of scores in the relevant cells and then dividing by the number of cases in those cells.
		The estimated marginal means for the A and B main effects are the unweighted means (cf.
	web.uccs.edu /lbecker/SPSS/glm_uneqn.htm (2574 words)

	Texas Property Value Study - 1999 Preliminary Report
		Dividing the former by the latter produces the weighted mean appraisal ratio of 0.8216.
		A value-stratified weighted mean appraisal ratio is a mechanism to automatically adjust the sample to be representative of the population from which it is taken.
		A weighted mean ratio is calculated for the entire property category by dividing the sum of the CAD values in every strata by the sum of the PTD values in every strata.
	www.window.state.tx.us /taxinfo/proptax/pvs00/tc2.html (2781 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)

	Weighted comparison of means - Statistics Notes British Medical Journal - Find Articles
		Note that the weighted mean, 79.50, is not the same as the unweighted mean in the table, 81.6.
		Here we calculate the weighted sum of the observations squared, then subtract the number of observations times the weighted mean squared.
		For the second group, the weighted sum of the observations squared is 3 751 934/(704/17) = 90 600.68 and the sum of squares about the mean is 90 600.68 - 17 x [72.51.sup.2] 1219.78.
	www.findarticles.com /p/articles/mi_m0999/is_n7125_v316/ai_20180145 (799 words)

	Exotic means, standard deviation, etc.
		The mean we’ve looked at so far is known as the arithmetic mean; it functions by adding together the scores, and dividing by the number of scores.
		Weighted means are useful for determining the mean of data that is presented in a relative frequency table.
		The mean of the data is the mean of the values in the table, using the relative frequencies as weights.
	www.sscnet.ucla.edu /ssc/labs/brenner/econ40/sdhandout.htm (1012 words)

	Lecture Notes 3 (Site not responding. Last check: 2007-09-10)
		For example, to compute the arithmetic mean of a sample of numbers, such as 19, 20, 21, 23, 18, 25, and 26, first sum the numbers: (19+20+21+23+18+25+26) = 152, and then calculate the sample mean by dividing this total (152) by the number of observations (7), which gives a mean of 21.7 or about 22.
		Even though the mean is sensitive to extreme values (i.e., extremely large or small data can cause the mean to be pulled toward the extreme data) it is still the most widely used measure of location.
		For example, the sum of the deviations of the numbers in a set of data from the mean is zero, and the sum of the squared deviations of the numbers in a set of data from the mean is minimum value.
	business.clayton.edu /arjomand/business/l3.html (1973 words)

	Weighted mean difference (Site not responding. Last check: 2007-09-10)
		The weight given to each study (how much influence each study has on the overall results of the meta-analysis) is determined by the precision of its estimate of effect and, in the statistical software in RevMan and CDSR, is equal to the inverse of the variance.
		The weighted mean could be calculated for groups before and after an intervention (like blood pressure lowering), and the weighted mean difference would be the difference between start and finish values.
		This is a defence against giving undue weight to small studies of low variance, where there may have been less than robust treatment of data, and where people could have cheated.
	www.jr2.ox.ac.uk /Bandolier/booth/glossary/wmd.html (248 words)

	Texas Property Value Study - 2000 Preliminary Report
		The weighted mean and simple mean are calculated for comparison to the stratified weighted mean to be calculated in Table Four and for use in calculating the price-related differential (PRD).
		Table Three also shows how the weighted mean stratum ratios are calculated by dividing the CAD value in each stratum by the PTD value in each stratum.
		Table Four also shows the calculation of the stratified weighted mean ratio by dividing the sum of the CAD values for each stratum by the sum of the PTD market value estimated for each stratum.
	www.window.state.tx.us /taxinfo/proptax/pvs01/pv2.htm (2806 words)

	PlanetMath: weighted power mean (Site not responding. Last check: 2007-09-10)
		The weighted power mean is a continuous function of
		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
		This is version 7 of weighted power mean, born on 2001-10-17, modified 2005-01-30.
	planetmath.org /encyclopedia/WeightedPowerMean.html (120 words)

	Technology in Education
		The mean number of students in the sample of studies was 184, and the range was from 32 to 2,802.
		Table 2a and Table 2b list the mean study-weighted means and the unweighted means for each of the three outcomes and the overall mean.
		Finally, the mean study-weighted effect size for the three study-weighted comparisons that contained behavioral outcomes was -.091, (p >.05), with a 95-percent confidence interval of -.142 to 1.243, indicating that technology had a slight, negative, nonsignificant effect on students' behavioral outcomes.
	www.ncrel.org /tech/effects2/results.htm (915 words)

	Definition: Weighted mean (Site not responding. Last check: 2007-09-10)
		The weighted mean is a mean where there is some variation in the relative contribution of individual data values to the mean.
		Data values with larger weights contribute more to the weighted mean and data values with smaller weights contribute less to the weighted mean.
		To restore balance, you would place less weight on the over represented segments of the population and greater weight on the under represented segments of the population.
	www.childrens-mercy.org /stats/definitions/weightedmean.htm (173 words)

	Weighted Samples - GNU Scientific Library -- Reference Manual
		The sample weight w_i is defined as the reciprocal of this variance, w_i = 1/\sigma_i^2.
		Setting a weight to zero corresponds to removing a sample from a dataset.
		In this case the estimator for the variance replaces the sample mean \Hat\mu by the known population mean \mu,
	www.gnu.org /software/gsl/manual/html_node/Weighted-Samples.html (432 words)

	Method of and apparatus for image smoothing along a tangential direction of a contour - Patent 5050227
		According to an aspect of the present invention, the weighting factors are further distributed in a normal direction perpendicular to the tangential direction, and the weighting factors enhance detail of the image in the second direction.
		The weighting factors except for one for the cental pixel have values which are obtained by multiplying the corresponding weighting factors of the S/E filters SEF1a-SEF1d by a coefficient b; this corresponds to the operation in the multiplication units 92a-92d shown in FIG.
		The weighting factors for the pixels within one pixel width in the normal direction Y from the contour, which is a center line of the matrix in the tangential direction X, have values of a first sign (plus in FIGS.
	www.freepatentsonline.com /5050227.html (4928 words)

	Jenness Enterprises - ArcView Extensions; Weighted Mean
		This extension creates a new button on the VIEW toolbar which enables you to calculate the weighted mean of a group of points.
		Weighted Mean uses the following equations to calculate the weighted mean center of a cluster of points.
		Both the RESULTS table and the Shapefile Point Attribute Table will contain a single record containing the name of the Weighting Field, the number of records used in the analysis, and the X and Y coordinates of the weighted mean center.
	www.jennessent.com /arcview/weighted_mean.htm (1035 words)

	Dissecting the Decline: A "share-weighting" analysis gives a better read on the market's vital signs than major market ...
		The mean return of all stocks, bolstered by mid- and small-cap companies, was 1.1%, and the median return improved (compared to the prior two years) to -2.4%.
		Nevertheless, the mean return was a paltry 2.8%, and the median return was -12.5%.
		Weighting a portfolio according to market cap (which is the mandate of both the S&P 500 and the Wilshire 5000) is understandable.
	www.financial-planning.com /pubs/fp/20021001015.html (1899 words)

	Statistics
		The mean or average is the sum of values divided by the total number of values.
		The average or mean is the sum of the scores divided by 4.
		The grade of an A is weighted as 4, a B is weighted as 3, a C is weighted as 2, and a D is weighted as 1.
	www.omegamath.com /Data/d4.1.html (750 words)

	The UNIVARIATE Procedure : Statistical Computations
		To test that the new analysis variable's mean or median equals zero is equivalent to the test that the means or medians of the two original variables are equal.
		For a symmetric distribution, the symmetrically Winsorized mean is an unbiased estimate of the population mean.
		For a symmetric distribution, the symmetrically trimmed mean is an unbiased estimate of the population mean.
	www.okstate.edu /sas/v7/sashtml/books/pguide/zte-comp.htm (2471 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)

	Mean - Wikipedia, the free encyclopedia
		The mean number of legs is going to be less than 2, because there are amputees with one leg or no legs, but no people with more than two legs.
		An unweighted mean can be turned into a weighted mean by repeating elements.
		This connection can also be used to state that a mean is the weighted version of an unweighted mean.
	en.wikipedia.org /wiki/Mean (1373 words)

	Jenness Enterprises - ArcView Extensions; 3D Weighted Mean
		This extension creates a new button on the VIEW toolbar which enables the user to calculate the 3D weighted mean of a group of points.
		Jenness, J. 3d weighted mean of points (weightmean3d.avx) extension for ArcView 3.x, v.
		Both the RESULTS table and the Shapefile Point Attribute Table will contain a single record containing the name of the Weighting Field, the number of records used in the analysis, and the X, Y, and Z coordinates of the weighted mean center.
	www.jennessent.com /arcview/3d_weighted_mean.htm (1207 words)

	v5n1
		Moreover, some inequalities involving the arithmetic mean, the harmonic mean, the logarithmic mean, and comparison between the extended mean values and the generalized weighted mean with two parameters and constant weight are obtained.
		The extended mean values E(r, s; x, y) play an important role in theory of mean values and theory of inequalities, and even in the whole mathematics, since many norms in mathematics are always means.
		Some bounds for the derivation of the integral mean of a function defined on a compact disk from the value at the central point and related results are presented.
	rgmia.vu.edu.au /v5n1.html (988 words)

	Weighted Arithmetic Mean (Site not responding. Last check: 2007-09-10)
		a numeric vector containing the values whose mean is to be computed.
		a vector of weights the same length as
		giving the weights to use for each element of
	www.math.montana.edu /Rweb/Rhelp/weighted.mean.html (42 words)

	Weighted comparison of means -- Bland and Kerry 316 (7125): 129 -- BMJ (Site not responding. Last check: 2007-09-10)
		Weighted comparison of means -- Bland and Kerry 316 (7125): 129 -- BMJ
		Note that the weighted mean, 79.50, is not the same as
		the weighted estimates of the means and common variance in the
	www.bmj.com /cgi/content/full/316/7125/129 (820 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/Feb96/opc.static/geometric_mean.html (823 words)

	Weighted Mean (via CobWeb/3.1 planetlab2.cs.unc.edu) (Site not responding. Last check: 2007-09-10)
		If we wanted to find the mean length of service for these 18 people, we could add 15 + 15 +…+ 15 + 20 +…+ 20 + 25 +…+ 25 + 30, then divide the total by 18.
		But we could also use the weighted mean.
		15 is a value, and 8 is its weight.
	infinity.cos.edu.cob-web.org:8888 /faculty/woodbury/Stats/Tutorial/CT_WeightedMean.htm (170 words)

	GNU Scientific Library -- Reference Manual - Weighted Samples (Site not responding. Last check: 2007-09-10)
		The functions accept an array of samples, @math{x_i}, with associated weights, @math{w_i}.
		The sample weight @math{w_i} is defined as the reciprocal of this variance, @math{w_i = 1/\sigma_i^2}.
		In this case the estimator for the variance replaces the sample mean @math{\Hat\mu} by the known population mean @math{\mu},
	www.math.utah.edu /software/gsl/gsl-ref_311.html (348 words)

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