In mathematics, the geometric mean is a mean or average, which indicates the central tendency or typical value of a set of numbers by using the product of their values. The geometric mean is defined as the nth root of the product of n numbers, i.e. for a set of numbers x1, x2... xn, the geometric mean is defined as 1 n = x 1 x 2 ⋯ x n n For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, 2 ⋅ 8 = 4. As another example, the geometric mean of the three numbers 4, 1, 1/32 is the cube root of their product, 1/2, that is, 4 ⋅ 1 ⋅ 1 / 32 3 = 1 / 2. A geometric mean is 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 value to compare two companies which are each rated at 0 to 5 for their environmental sustainability, are rated at 0 to 100 for their financial viability. If an arithmetic mean were used instead of a geometric mean, the financial viability would have greater weight because its numeric range is larger.
That is, a small percentage change in the financial rating makes a much larger difference in the arithmetic mean than a large percentage change in environmental sustainability. The use of a geometric mean normalizes the differently-ranged values, meaning 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, a and b, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a and b. The geometric mean of three numbers, a, b, c, is the length of one edge 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 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 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 The geometric mean of a data set is given by: 1 n = a 1 a 2 ⋯ a n n; the above figure uses capital pi notation to show a series of multiplications. Each side of the equal sign shows that a set of values is multiplied in succession to give a total product of the set, the nth root of the total product is taken to give the geometric mean of the original set. For example, in a set of four numbers, the product of 1 × 2 × 3 × 4 is 24, the geometric mean is the fourth root of 24, or ~ 2.213. The exponent 1 n on the left side is equivalent to the taking nth root. For example, 24 1 4 = 24 4; the geometric mean of a data set is less than the data set's arithmetic mean unless all members of the data set are equal, in which case the geometric and arithmetic means are equal.
This allows the definition of the arithmetic-geometric mean, an intersection of the two which always lies in b
Kathy E. Ferguson is an American author, political theorist and Fulbright Grant recipient, she is women's studies at the University of Hawai'i at Manoa. In 2009, the American Political Science Association recognized Ferguson for her research in the field of feminist political theory, her more notable books include Emma Goldman: Political Thinking in the Streets, The Man Question: Visions of Subjectivity in Feminist Theory, Kibbutz Journal: Reflections on Gender and Militarism in Israel, a work of political theory written in the personal essay form while living with her husband and two young sons on a kibbutz in Israel. Ferguson's writing brings activist strategies and tactics, feminist cultural artifacts, practices of domestic or everyday life into the canon of political theory. Ferguson received a B. A. in political science in 1972 from Purdue University. She received a doctorate in political science from the University of Minnesota in 1976, writing the first feminist dissertation in the department.
Ferguson has taught at Siena College in Albany, New York, the Institute for Advanced Studies in Vienna and the University of Gothenburg, Sweden. She teaches at the University of Hawaii, where she serves as Chair of the Political Science Department. Ferguson received a Fulbright appointment at Ben Gurion University in Beer Sheva, Israel in 1999. In 2009, The American Political Science Association's Women and Political Research Section awarded her the Okin-Young Prize, recognizing the year's "best paper on feminist political theory published in an English language academic journal." The award recognized an article that would serve as the basis for the book Emma Goldman: Political Thinking in the Streets. The book was the result of research conducted with the help of the Emma Goldman Papers Project at the University of California, Berkeley. Ferguson is involved with the International Dyslexia Association in which she volunteers to tutor dyslexic children and adults. Ferguson's research intertwines political science.
Her books include: Emma Goldman: Political Thinking in the Streets, written in 2011. Gender and Globalization in Asia and the Pacific, co-edited with Monique Mironesco 2008. Oh, Can You See? The Semiotics of the Military in Hawaii, written with Phyllis Turnbull 1995. Kibbutz Journal: Reflections on Gender and Militarism in Israel, written in 1995; the Man Question: Visions of Subjectivity in Feminist Theory, written in 1993. The Feminist Case Against Bureaucracy, written in 1984
The Circuit Trois-Rivières is a street circuit located in Trois-Rivières, Quebec and has been the home of the annual Grand Prix de Trois-Rivières since 1967. The circuit is located on the Terrain de l'Exposition and is unusual in that it passes through Porte Duplessis, the narrow concrete gateway of the grounds at turn 3. Throughout its history the circuit has hosted numerous major North American racing series including the American Le Mans Series, the Grand-Am Rolex Sports Car Series, the Trans-Am Series, Can-Am, Indy Lights and Formula Atlantic; the Grand Prix has been headlined by the NASCAR Pinty's Series since 2007, in 2014 was expanded to two weekends when it was joined by the FIA World Rallycross Championship and its World RX of Canada race. Rallycross Weekend FIA World Rallycross Championship – World RX of Canada AMA Supermoto National Championship Series Americas Rallycross Championship Formula Drift Canada NASA Challenge Xtreme Elite Elka SuperquadsCircuit Weekend NASCAR Pinty's Series F3 Americas Championship Canadian Touring Car Championship IMSA Prototype Challenge presented by Mazda IMSA GT3 Cup Challenge Canada Nissan Micra Cup Formula Tour 1600 SCCA Trans-Am Series SCCA Can-Am Series SCCA World Challenge SCCA North American Touring Car Championship IMSA American Le Mans Series Grand-Am Rolex Sports Car Series Grand-Am KONI Sports Car Challenge Atlantic Championship IndyCar Indy Lights IndyCar Pro Mazda Championship Formula Super Vee Official website NASCAR Track Page Ultimate Racing History - Circuit Trois-Rivières Racing Sports Cars - Trois-Rivières - List of Races