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Topic: Geometric mean

Related Topics

Weighted geometric mean

Geometric standard deviation

Arithmetic mean

Generalized mean

Inequality of arithmetic and geometric means

Weighted harmonic mean

Harmonic mean

Weighted mean

Lognormal distribution

Standard deviation

Normal distribution

Weight function

Hyperbolic coordinates

Logarithmic identities

Logarithmic scale

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	How to Calculate Geometric Mean
		A geometric mean, unlike an arithmetic mean, tends to dampen the effect of very high or low values, which might bias the mean if a straight average (arithmetic mean) were calculated.
		Geometric mean is often used to evaluate data covering several orders of magnitude, and sometimes for evaluating ratios, percentages, or other data sets bounded by zero.
		For example, to calculate the geometric mean of the values +12%, -8%, and +2%, instead calculate the geometric mean of their decimal multiplier equivalents of 1.12, 0.92, and 1.02, to compute a geometric mean of 1.0167.
	www.buzzardsbay.org /geomean.htm (3272 words)

	Geometric mean - Psychology Wiki
		The geometric mean of a set of positive data is defined as the nth root of the product of all the members of the set, where n is the number of members.
		The geometric mean of a data set is always smaller than or equal to the set's arithmetic mean (the two means are equal if and only if all members of the data set are equal).
		It is not the arithmetic mean, because what these numbers mean is that on the first year your investment was multiplied (not added to) by 1.10, on the second year it was multiplied by 1.50, and the third year it was multiplied by 1.30.
	psychology.wikia.com /wiki/Geometric_mean (612 words)

	PlanetMath: mean (Site not responding. Last check: )
		Loosely speaking, a mean is a way to describe a collection of numbers such that the mean in some sense describe the “average”; entry of these numbers.
		Pythagoras identified three types of means: the arithmetic mean, the geometric mean, and the harmonic mean.
		This is version 8 of mean, born on 2002-06-04, modified 2006-09-29.
	planetmath.org /encyclopedia/Mean3.html (189 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: )
		Sample mean is often used as an estimator of the central tendency such as the population mean.
		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 the most likely (mode).
		The generalized mean, also known as the power mean or HÃ¶lder mean, is an abstraction of the quadratic, arithmetic, geometric and harmonic means.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Mean (1416 words)

	[No title] (Site not responding. Last check: )
		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).
		Write a program to calculate the geometric mean to two decimal places without using any mathematical functions such as sqrt, log, exp, pow, or the like, by guessing the answer (call it G), then multiplying out G^n and comparing it to the product of the numbers.
		Thus, the geometric mean of the scores: 1, 2, 3, and 10 is the fourth root of 1 x 2 x 3 x 10 which is the fourth root of 60 which equals 2.78.
	www.lycos.com /info/geometric-mean.html?page=2 (441 words)

	Confidence Intervals Involving Logarithmically Transformed Data
		The mean of the logs estimates both the population mean and median in the log transformed scale.
		The confidence interval from the logged data estimates the difference between the population means of log transformed data, that is, it estimates the difference between the logs of the geometric means.
		Since the geometric mean is sometime an estimate of the median in the original scale, it follows that a confidence interval for the geometric means is approximately a confidence interval for the ratio of the medians in the original scale.
	www.tufts.edu /~gdallal/ci_logs.htm (881 words)

	Looking for the Mean: Using five-year rolling returns to calculate equity performance reduces volatility and presents a ...
		Note that the geometric mean is always lower than (and sometimes equal to) its arithmetic mean cousin, which was 13.1% in this case, over the same time time period.
		Geometric means represent a multiplicative function, while arithmetic returns are computed as an additive function.
		Interestingly, the arithmetic mean for the 29 five-year rolling returns (where the rolling returns are calculated as geometric mean returns) was 13.1%, which is identical to the arithmetic average return for the 33 annual returns.
	www.financial-planning.com /pubs/fp/20040901034.html (1060 words)

	The Super-Symmetric Mean
		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.
		To illustrate on a simple example, Figure 1 shows how the arithmetic and geometric means of the numbers 3 and 15 are related to the two polynomials that match the value and the derivative of the function f(x)=(x-3)(x-15) respectively at x=0.
	www.mathpages.com /home/kmath461.htm (768 words)

	Statistics of central tendency
		Taking the geometric mean of these numbers (1.216) and multiplying that by itself three times also gives the correct final height (1.80), while taking the arithmetic mean (1.24) times itself three times does not give the correct final height.
		The geometric mean is slightly smaller than the arithmetic mean; unless the data are highly skewed, the difference between the arithmetic and geometric means is small.
		The harmonic mean is less sensitive to a few large values than are the arithmetic or geometric mean, so it is sometimes used for variables such as dispersal distance.
	udel.edu /~mcdonald/statcentral.html (1437 words)

	Mean and Variance
		Hence the mean of the sum is the sum of the means.
		The geometric mean is used when the log of a measurement is a better indicator (for whatever reason) than the measurement itself.
		The average of 2, 5, 8, and 9 is 6, yet the geometric mean is 5.18.
	www.mathreference.com /pr,mean.html (1550 words)

	Question Corner -- Applications of the Geometric Mean
		It is not the arithmetic mean, because what these numbers mean is that on the first year your investment was multiplied (not added to) by 1.10, on the second year it was multiplied by 1.60, and the third year it was multiplied by 1.20.
		If you calculate this geometric mean you get approximately 1.283, so the average rate of return is about 28% (not 30% which is what the arithmetic mean of 10%, 60%, and 20% would give you).
		That means that during the first year of the investment you have the unreasonable calculation you described, but over the long term those effects are negligble.
	www.math.toronto.edu /mathnet/questionCorner/geomean.html (2387 words)

	Geometric mean arithmetic mean or means calculate center frequeny calculation average numbers bandwidth - sengpielaudio (Site not responding. Last check: )
		Comparison between the arithmetic mean (average) and the geometric mean.
		The geometric mean of three numbers is the cubic root of their product.
		The arithmetic mean is the sum of the numbers, divided by the quantity of the numbers.
	www.sengpielaudio.com /calculator-geommean.htm (225 words)

	Geometric Mean, Kalamazoo Michigan County Government Website, Environmental Health Bureau
		The Environmental Health Bureau uses the geometric mean to estimate the 30-day average from all individual samples taken during five or more sampling events.
		The geometric mean is another way to average a set of values and is commonly used with bacterial water assessment, which often show a great deal of variability.
		One benefit the geometric mean has over the arithmetic mean is that it (geometric mean) reduces the effect of an occasional high or low value on the average.
	www.kalcounty.com /eh/geometric-mean.htm (314 words)

	Geometric Nice?
		If the geometric mean is known, you can use it to find the value of another unknown in the proportion as is shown here.
		In this case, the geometric mean is 12.
		We can state with reasonable confidence that the altitude of the larger triangle is the geometric mean of the two segments of the hypotenuse of the larger triangle.
	www.mste.uiuc.edu /dildine/sketches/meanalt1.html (327 words)

	Geometric Meaning of the Geometric Mean
		The geometric mean then answers this question: given a rectangle with sides a and b, find the side of the square whose area equals that of the rectangle.
		The length of the perpendicular from the circumference to the diameter is exactly the geometric mean of a and b.
		The above construction of the mean proportional is based on a Corollary from Euclid VI.8: If in a right-angled triangle a perpendicular is drawn from the right angle to the base, then the straight line so drawn is a mean proportional between the segments of the base.
	www.cut-the-knot.org /pythagoras/GeometricMean.shtml (593 words)

	Arithmetic vs. Geometric Mean
		The geometric mean and standard deviation. The appropriate measures of growth-factor norms are the less-familiar geometric mean and standard deviation.
		The arithmetic mean and arithmetic standard deviation are sum-based values. As such, they are appropriate for additive processes. But earnings growth is not additive; it is multiplicative. The appropriate measures for EPS growth factors are the geometric mean and geometric standard deviation, which are product-based values.
		The arithmetic mean of these factors is 1.2584, implying that EPS grew at an average annual rate of 25.84%. Had that been so, the first EPS, $0.32, would have grown into $2.53 in the last year—which, of course, it did not.
	www.thinkingapplied.com /means_folder/deceptive_means.htm (1949 words)

	Means
		The term "mean" in mathematics simply reflects a specific relationship of one number as the middle point of two extremes.
		The geometric mean is similar, but based on a common multiplier that relates the mean to the other two numbers.
		As an example, the geometric mean of 2 and 8 is 4, as 4 is equally distant between the two in multiplication:
	goldennumber.net /means.htm (313 words)

	PlanetMath: geometric mean
		are real numbers, we define their geometric mean as
		See Also: arithmetic mean, general means inequality, weighted power mean, power mean, arithmetic-geometric-harmonic means inequality, root-mean-square, proof of general means inequality, derivation of zeroth weighted power mean, 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 2 of geometric mean, born on 2001-10-20, modified 2001-11-09.
	planetmath.org /encyclopedia/GeometricMean.html (94 words)

	Definition: Geometric mean
		It is different than the traditional mean (which we sometimes call the arithmetic mean) because it uses multiplication rather than addition to summarize data values.
		The geometric mean is a useful summary when we expect that changes in the data occur in a relative fashion.
		We can calculate the geometric means by computing 10 to the power of 0.7712 and 0.0294 respectively.
	www.childrensmercy.com /stats/definitions/geometric.htm (506 words)

	Geometric Mean (Site not responding. Last check: )
		The logarithm of the geometric mean is the arithmetic mean of the log transformed data:
		The geometric mean is an appropriate measure of central tendency when averages of rates or index numbers are required.
		The geometric mean is calculated from the arithmetic mean of the log transformed data.
	shazam.econ.ubc.ca /intro/gmean.htm (195 words)

	Ways of Means Committee: There's a critical difference between arithmetic and geometric means.
		But even though "average" is synonymous with "mean," one mean or average is appropriate for investments while the other is not.
		The geometric mean is the return that, if held constant, will generate the stipulated future value over the stated period.
		You see that as the standard deviation (or volatility) of annual returns increases, the arithmetic mean grows larger than (and therefore, further away from) the correct geometric mean.
	www.financial-planning.com /pubs/fp/20051101028.html (1102 words)

	Radicals Review and Intro to Geometric Mean
		We see that that the arithmetic mean is the number such that the difference or distance between all three numbers is the same, 10 - 4 = 6 and 16 - 10 = 6.
		The geometric mean is similar to the arithmetic mean, but the geometric mean of two numbers is the number such that the ratios between the three numbers is the same.
		The geometric mean between two positive numbers is a positive number such that when we divide the geometric mean by 4 it is gives us the same result as when we divide 16 by the geometric mean.
	jwilson.coe.uga.edu /EMT668/EMAT6680.Folders/Brooks/6690stuff/Righttriangle/radicalsrev.html (404 words)

	Arithmetic Mean, Harmonic Mean, Combined Average, Geometric Mean
		What this all means is that if the different samples intuitively should not have the same weights, yet the numerators are all the same, they should be considered as a fixed numerator over a varying denominator.
		The geometric mean is used in cases where the numbers are effectively multipliers rather than having an additive effect.
		A possible example might be if a modem's data compression compressed the data by a factor of 2:1 and then an application compressed the data some more at 3:1, you would use the geometric mean to derive the average compression.
	home.comcast.net /~b.giese/dc_mean.html (1135 words)

	Geometric Mean - Actuarial Outpost
		It is not the arithmetic mean, because what these numbers mean is that on the first year your investment was multiplied (not added to) by 1.10, on the second year it was multiplied by 1.60, and the third year it was multiplied by 1.20.
		If you calculate this geometric mean you get approximately 1.283, so the average rate of return is about 28% (not 30% which is what the arithmetic mean of 10%, 60%, and 20% would give you).
		People often read about much higher arithmetic means of more volatile investments like small cap stocks and are mislead to believe that they also translate into much higher geometric means.
	www.actuarialoutpost.com /actuarial_discussion_forum/showthread.php?p=1938552 (597 words)

	Definition: Geometric mean
		It is different than the traditional mean (which we sometimes call the arithmetic mean) because it uses multiplication rather than addition to summarize data values.
		The geometric mean is a useful summary when we expect that changes in the data occur in a relative fashion.
		Geometric means are often useful summaries for highly skewed data.
	www.childrens-mercy.org /stats/definitions/geometric.htm (506 words)

	Experimental CPI Using Geometric Means
		BLS currently is evaluating the full or partial adoption of the geometric mean formula in the CPIU and CPIW. The current CPI, which is calculated using a fixed-weight Laspeyres formula, does not reflect the fact that consumers can and do change spending patterns as relative prices change.
		BLS's best estimate is that use of the geometric mean formula in all CPI basic indexes would lower the growth rate of the index by approximately one-quarter of one percent per year.
		Partial adoption of the geometric mean formula would be expected to have a downward impact of between zero and one-quarter of one percent per year, depending on how many, and which, indexes continue to be based on the Laspeyres approach.
	www.bls.gov /cpi/cpigmsum.htm (897 words)

	MAT 300 Some Pythagorean Means
		The arithmetic mean of two numbers exceeds the smaller number by the same as the larger number exceeds the mean. I.e., A is the arithmetic mean of a and b, a
		Equivalently, in our modern definition, G is the geometric mean of a and b if the ratio of the first number to the geometric mean is the same as the ratio of the mean to the second, or a:G = G:b. I.e.,
		So 6 is the geometric mean of 2 and 18 since
	www.southernct.edu /~gingrich/mat3002005/pythagoreanmeans.html (142 words)

	Geometric Mean calculation - MQL4 advice needed - Forex Trading Software Forum
		I refer you to http://www.buzzardsbay.org/geomean.htm which shows a few ways to do the calculation of geometric mean.
		Oh yes - my reason for this is to get a 'mean' that is not effected by large or small data points on the left/right of the dataset - as this would have the effect of skewing the mean towards these large/small datums.
		I did google on calculating 'mean' and the geometric mean filters/softens the impact of for example a few large numbers in a dataset of say, smallish numbers (much like the example above where 1200 is LARGE and 6,50,9 are smal)
	www.metaquotes.net /forum/1349 (531 words)

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