** Geometric Mean vs Arithmetic Mean
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In mathematics and statistic, mean is used to represent data meaningfully. In addition to these two fields, mean is used very often in many other fields too, such as economy. Both arithmetic mean and geometric mean are very often referred as average, and are methods to derive central tendency of a sample space. The most obvious difference between arithmetic mean and geometric mean is the way they are calculated.

Arithmetic mean of a set of data is calculated by dividing the sum of all the numbers in the data set by the count of those numbers.

For example, the arithmetic mean of the data set {50, 75, 100} is (50+75+100)/3, which is 75.

Geometric mean of a data set is calculated by taking the nth root of the multiplication of all the numbers in the data set , where ‘n’ is the total number of data points in the set that we considered. Geometric mean is applicable only on a set of positive numbers.

For example, the geometric mean of the data set {50, 75, 100} is ³_{√}(50x75x100), which is approximately 72.1.

For a set of data, if we calculate both the arithmetic and geometric means, it is clear that geometric mean is either same or less than the arithmetic mean. Arithmetic mean is more appropriate to calculate the mean value of the outputs of a set of independent events. In other words, if one data value in the data set has no effect on any other data value in the set, then it is a set of independent events. Geometric mean is used in instances where the difference among data values of the corresponding data set is multiple of 10 or logarithmic. In the world of finance, in particular instance, geometric mean is more appropriate to calculate the mean. In geometry, the geometric mean of two data values is representing the length between the data values.

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