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GEOMETRIC MEAN
Geometric mean can be defined as the 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. It is often used when comparing different items and finding a single for these items when each item has multiple properties which have different numeric ranges.
An arithmetic mean is used instead of this when the financial viability is given more weight. This is because its numeric range is larger- so a small percentage change in the financial rating makes a much larger difference in the arithmetic mean than that of a large percentage change in environmental sustainability.
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The use of this can "normalize" the ranges being averaged so that no range dominates the weighting and a given percentage change in any of the properties have the same effect on the geometric mean.
It is similar to the arithmetic mean except that the numbers are multiplied and then the Nth root where n is the count of numbers in the set of the resulting product, s taken and the geometric mean can also be understood in terms of geometry.
The geometric mean of two numbers such as 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 and the geometric mean of three numbers such as a, b, and c, 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.
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It applies only to positive numbers and it is also often used for a set of numbers whose values are meant to be multiplied together or are exponential in nature. For a data set, this is denoted as follows
The geometric mean of a data set inequality of arithmetic as well as geometric means the data set's arithmetic mean unless all members of the data set are equal. In this case, the geometric and arithmetic means are equal and this allows the definition of the Arithmetic-geometric mean is a mixture of the two which always lies in between.
