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- Geometric_mean abstract "In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root (where n is the count of numbers) of the product of the numbers.For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is . As another example, the geometric mean of the three numbers 4, 1, and 1/32 is the cube root of their product (1/8), which is 1/2; that is .A geometric mean is often used when comparing different items – finding a single "figure of merit" for these items – when each item has multiple properties that have different numeric ranges. For example, the geometric mean can give a meaningful "average" to compare two companies which are each rated at 0 to 5 for their environmental sustainability, and are rated at 0 to 100 for their financial viability. If an arithmetic mean were used instead of a geometric mean, the financial viability is given more weight because its numeric range is larger- so a small percentage change in the financial rating (e.g. going from 80 to 90) makes a much larger difference in the arithmetic 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 can be understood in terms of geometry. The geometric mean of two numbers, and , is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths and . Similarly, the geometric mean of three numbers, , , and , is the length of one side of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers.The geometric mean applies only to positive numbers. It is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature, such as data on the growth of the human population or interest rates of a financial investment.The geometric mean is also one of the three classical Pythagorean means, together with the aforementioned arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic 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 (see Inequality of arithmetic and geometric means.)".
- Geometric_mean thumbnail Geometric_mean_3D_plot_from_0_to_100.png?width=300.
- Geometric_mean wikiPageExternalLink GeometricMean.html.
- Geometric_mean wikiPageExternalLink geomean.htm.
- Geometric_mean wikiPageExternalLink how.html.
- Geometric_mean wikiPageExternalLink means.shtml.
- Geometric_mean wikiPageExternalLink GeometricMean.shtml.
- Geometric_mean wikiPageExternalLink geomean.php3.
- Geometric_mean wikiPageExternalLink geomean.html.
- Geometric_mean wikiPageExternalLink calculator-geommean.htm.
- Geometric_mean wikiPageID "13046".
- Geometric_mean wikiPageRevisionID "602567424".
- Geometric_mean hasPhotoCollection Geometric_mean.
- Geometric_mean subject Category:Means.
- Geometric_mean comment "In mathematics, the geometric mean is a type of mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values (as opposed to the arithmetic mean which uses their sum). The geometric mean is defined as the nth root (where n is the count of numbers) of the product of the numbers.For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is .".
- Geometric_mean label "Geometric mean".
- Geometric_mean label "Geometrisches Mittel".
- Geometric_mean label "Media geométrica".
- Geometric_mean label "Meetkundig gemiddelde".
- Geometric_mean label "Moyenne géométrique".
- Geometric_mean label "Média geométrica".
- Geometric_mean label "Średnia geometryczna".
- Geometric_mean label "Среднее геометрическое".
- Geometric_mean label "متوسط هندسي".
- Geometric_mean label "几何平均数".
- Geometric_mean label "幾何平均".
- Geometric_mean sameAs Geometrický_průměr.
- Geometric_mean sameAs Geometrisches_Mittel.
- Geometric_mean sameAs Media_geométrica.
- Geometric_mean sameAs Batezbesteko_geometriko.
- Geometric_mean sameAs Moyenne_géométrique.
- Geometric_mean sameAs 幾何平均.
- Geometric_mean sameAs 기하_평균.
- Geometric_mean sameAs Meetkundig_gemiddelde.
- Geometric_mean sameAs Średnia_geometryczna.
- Geometric_mean sameAs Média_geométrica.
- Geometric_mean sameAs m.03dzv.
- Geometric_mean sameAs Q185049.
- Geometric_mean sameAs Q185049.
- Geometric_mean wasDerivedFrom Geometric_mean?oldid=602567424.
- Geometric_mean depiction Geometric_mean_3D_plot_from_0_to_100.png.
- Geometric_mean isPrimaryTopicOf Geometric_mean.
