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In mathematics, the harmonic mean (sometimes called the subcontrary mean) is one of several kinds of average, and in particular one of the Pythagorean means. Typically, it is appropriate for situations when the average of rates is desired. The harmonic mean can be expressed as the reciprocal of the arithmetic mean of the reciprocals. As a simple example, the harmonic mean of 1, 2, and 4 is 3 1 1 + 1 2 + 1 4 = 1 1 3 ( 1 1 + 1 2 + 1 4 ) = 12 7 .
From the third formula in the above equation, it is more apparent that the harmonic mean is related to the arithmetic and geometric means.Equivalently, the harmonic mean is the reciprocal of the arithmetic mean of the reciprocals.As a simple example, the harmonic mean of 1, 2, and 4 is.The Harmonic mean is a Schur-concave function, and dominated by the minimum of its arguments, in the sense that for any positive set of arguments, Thus, the harmonic mean can not be made arbitrarily large by adding more big values to the argument set.he harmonic mean is related to the other Pythagorean means, as seen in the third formula in the above equation. This is noticed if we interpret the denominator to be the arithmetic mean of the product of numbers n times but each time we omit the j th term.