The harmonic mean also called harmonic average, in the total numbers of items of variable divided by the sum of r reciprocals of the values of the variable. In the words of W. I.G reenwald, the harmonic mean is defined as the reciprocal of the arithmetic mean of the reciprocals of a serried. For its calculations we must first learn the reciprocals.
Reciprocals the reciprocal of a value is that quotient obtained by diving i with the given value. For example, reciprocal of the value 2 will be ½ or 0.5 of the value 1/4 or 0.25 and so on .Reciprocals can be computed with the help of tables given in appendix with the tables in appendix.
Use of Harmonic Mean:
This measure of averages can be used in the following cases:
(1) To compute average speed. When speed is given in kilometres per hour, distance is variable and time is constant. On the other hand when speed is given in minutes for each kilometric time is variable and distance would be constant.
(2) To find out average of prices: When rate may be as follows:
(3) To study about velocity etc, it is a useful average. In short we may say that harmonic mean is useful in averaging rates and ratios where time factor is variable and the act being performed ( say distance covered )is constant. The example given will clarify this point.