The difference between Geometric mean and Harmonic mean
When used as nouns, geometric mean means a measure of central tendency of a set of n values computed by extracting the nth root of the product of the values, whereas harmonic mean means a type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, h = { n \over {1 \over x_1} + {1 \over x_2} + \cdots {1 \over x_n} }.
check bellow for the other definitions of Geometric mean and Harmonic mean
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Geometric mean as a noun (mathematics):
A measure of central tendency of a set of n values computed by extracting the nth root of the product of the values.
Examples:
"The geometric mean of 2, 4 and 1 is <math>\sqrt[3]{2 \times 4 \times 1}</math> = 2"
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Harmonic mean as a noun (mathematics):
A type of measure of central tendency calculated as the reciprocal of the mean of the reciprocals, ie, H = { n \over {1 \over x_1} + {1 \over x_2} + \cdots {1 \over x_n} }
Examples:
"If ''a''<sub>''n''</sub> and ''b''<sub>''n''</sub> denote the perimeters of inscribed and circumscribed regular ''n''-gons, respectively, along some circle then the harmonic mean and geometric mean of those two perimeters yield the perimeters of the inscribed and circumscribed regular 2''n''-gons, respectively, along that same circle. (This is Archimedes' Recurrence Formula.)"