The harmonic mean is a measure of central tendency that is particularly useful for sets of numbers that are defined in relation to some unit, such as rates or ratios. It is defined as the reciprocal of the arithmetic mean of the reciprocals of a set of numbers. To calculate the harmonic mean of a set of \( n \) numbers \( x_1, x_2, ...
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The harmonic mean of positive numbers is . The Jensen inequality for gives , with equality exactly when all entries coincide.