The difference between Contraharmonic mean and Harmonic mean
When used as nouns, contraharmonic mean means a type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie. c = { {( x_1^2 + x_2^2 + ... + x_n^2) \over n } \over { ( x_1 + x_2 + ... + x_n ) \over n } }\ or \ c(x_1, x_2, ..., x_n) ={ { x_1^2+x_2^2+...+x_n^2} \over {x_1+x_2+...+x_n }}, 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 Contraharmonic mean and Harmonic mean
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Contraharmonic mean as a noun (mathematics):
A type of average calculated as the arithmetic mean of the squares of the values divided by the arithmetic mean of the values, ie. C = { {( x_1^2 + x_2^2 + ... + x_n^2) \over n } \over { ( x_1 + x_2 + ... + x_n ) \over n } }\ or \ C(x_1, x_2, ..., x_n) ={ { x_1^2+x_2^2+...+x_n^2} \over {x_1+x_2+...+x_n }}
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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.)"