The harmonic mean also arises when a circuit contains multiple resistors in parellel. For example, with three parellel resistors of resistance A, B and C ohms respectively, the equivilant resistance of the unit is
R = 1 / (1/A + 1/B + 1/C)
Consequently, the equivilant resistance is always less than that of any of the individual resistors. The reason for the equation is obvious when you consider what portion of current goes through each resistor, and therefore what resistance is applied to each portion of the current.
Clearly, the harmonic mean is undefined if any of the elements are 0, because division by 0 is undefined. However, the integrity of the formula for resistance is maintained because nothing really has no resistance (outside the bizarre world of superconducters), although connecting wires themselves are usually treated as such.
Because the harmonic mean is lower than any of the individual elements, it is useful (theoretically) for giving false impressions about data. Although this would rarely occur in a real situation, I remember using it in a statistics homework about using averages to make data appear favourable :)