Harmonic Mean: It is defined as the reciprocal of the arithmetic mean of the reciprocal of the individual observations.
Merits of H.M.:
1. Like AM and GM, it is also based on all observations.
2. It is most appropriate average under conditions of wide variations among the items of a series since it gives larger weight to smaller items.
3. It is capable of further algebraic treatment.
4. It is extremely useful while averaging certain types of rates and ratios.
Demerits of H.M.:
1. It is difficult to understand and to compute.
2. It cannot be computed when one of the values is 0 or negative.
3. It is necessary to know all the items of a series before it can be calculated.
4. It is usually a value which may not be a member of the given set of numbers.
Uses of H.M.:
If there are two measurements taken together to measure a variable, HM can be used. For example, tonne mileage, speed per hour. In the above example tonne mileage, tonne is one measurement and mileage is another measurement. HM is used to calculate average speed.