Defined as the nth root of the product of n numbers, i.e., for a set of numbers.
The geometric mean applies only to numbers of the same sign. 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 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. The geometric median of a discrete set of sample points in a Euclidean space is the point minimizing the sum of distances to the sample points. This generalizes the median, which has the property of minimizing the sum of distances for one-dimensional data, and provides a central tendency in higher dimensions. The geometric median may in turn be generalized to the problem of minimizing the sum of weighted distances, known as the Weber problem after Alfred Weber 's discussion of the problem in his 1909 book on facility location. DEFINITION of 'Geometric Mean'. The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. Technically defined as the 'n'th root product of 'n' numbers, the formula for calculating geometric mean is most easily written as: The Geometric Mean. In this video, I show how to find the geometric mean of two numbers and show what that number means in relation to the numbers that you started with. 1  Education. 2  Standard YouTube License. The geometric mean is NOT the arithmetic mean and it is NOT a simple average. It is the nth root of the product of n numbers. That means you multiply a bunch of numbers together, and then take the nth root, where n is the number of values you just multiplied. Naturally, the geometric mean can get very complicated. Here's a mathematical definition of the geometric mean: Remember that the capital PI symbol means to multiply a series of numbers. That definition says to multiply k numbers and then take the kth root. The geometric mean is defined as the nth root of the product of n numbers, i.e., for a set of numbers, the geometric mean is defined as. For instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product; that is. 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. The main benefit to using the geometric mean is that the actual amounts invested do not need to be known; the calculation focuses entirely on the return figures themselves and presents an apples-to-apples comparison when looking at two investment options. RELATED TERMS. The average of a set of products, the calculation of which is commonly used to determine the performance results of an investment or portfolio. Technically defined as the 'n'th root product of 'n' numbers, the formula for calculating geometric mean is most easily written as:
https://en.wikipedia.org/wiki/Geometric_mean https://en.wikipedia.org/wiki/Geometric_median http://www.investopedia.com/terms/g/geometricmean.asp http://www.youtube.com/watch?v=_UdGUULKN-E http://www.freemathhelp.com/geometric-mean.html https://en.wikipedia.org/wiki/Geometric_mean http://www.investopedia.com/terms/g/geometricmean.asp
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