The harmonic mean of a given set of data values is the reciprocal of the arithmetic mean of the reciprocals of the given observations. For example, if we are given the set of data values 2, 4, and 8 then the harmonic mean is calculated as, H = \frac{3}{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}}= \frac{3}{\frac{7}{8}} = \frac{24}{7} = 3.4285 We now list out some of the merits, demerits and applications of the harmonic mean.
Advantages of Harmonic Mean:
- The harmonic mean is rigidly defined.
- It is based on all the observations.
- It is suitable for further mathematical treatment.
- Since the reciprocals of the values of the variable are involved, it gives greater weightage to smaller observations and as such is not very much affected by one or two big observations.
- It is not affected very much by fluctuations of sampling.
- It is particularly useful in averaging special types of rates and ratios where time factor is variable and the act being performed remains constant.
Disadvantages of Harmonic Mean:
- It is not easy to understand and calculate.
- Its value cannot be obtained if any one of the observations is zero.
- It is not a representative figure of the distribution unless the phenomenon requires greater weightage to be given to smaller items. As such, it is hardly used in business problems.
Uses of Harmonic Mean:
- The harmonic mean is especially useful in averaging rates and ratios where the time factor is variable and the act being performed (e.g., distance) is constant.
- If different distances are traveled with corresponding different speeds, then the average speed is given by the weighted harmonic mean of the speeds, and the corresponding weights beings the distances covered.
