Editing 2435: Geothmetic Meandian
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==Explanation== | ==Explanation== | ||
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There are a number of different ways to identify the "{{w|average}}" value of a series of values, the most common unweighted methods being the {{w|median}} (take the central value from the ordered list of values if there are an odd number - or the value half-way between the two that straddle the divide between two halves if there are an even number) and the {{w|arithmetic mean}} (add all the numbers up, divide by the number of numbers). The {{w|geometric mean}} is less well-known but works similarly to the arithmetic mean. The geometric mean of ''n'' positive numbers is the ''n''th root of the product of those numbers. If all of the numbers in a sequence are identical, then its arithmetic mean, geometric mean and median will be identical, since they would all be equal to the common value of the terms of the sequence. However, if the sequence is not constant, then {{w|Inequality_of_arithmetic_and_geometric_means#Geometric_interpretation|the arithmetic mean will be greater than the geometric mean}}, and the median may be different than either of those means. | There are a number of different ways to identify the "{{w|average}}" value of a series of values, the most common unweighted methods being the {{w|median}} (take the central value from the ordered list of values if there are an odd number - or the value half-way between the two that straddle the divide between two halves if there are an even number) and the {{w|arithmetic mean}} (add all the numbers up, divide by the number of numbers). The {{w|geometric mean}} is less well-known but works similarly to the arithmetic mean. The geometric mean of ''n'' positive numbers is the ''n''th root of the product of those numbers. If all of the numbers in a sequence are identical, then its arithmetic mean, geometric mean and median will be identical, since they would all be equal to the common value of the terms of the sequence. However, if the sequence is not constant, then {{w|Inequality_of_arithmetic_and_geometric_means#Geometric_interpretation|the arithmetic mean will be greater than the geometric mean}}, and the median may be different than either of those means. |