Harmonic Mean

The harmonic mean is based on the reciprocals of the numbers averaged. It is defined as the reciprocal of the arithmetic means of the reciprocal of the individual observations. Where the number of items is large the computation of harmonic mean in the above manner because tedious.

Merits and Limitations of Harmonic Mean

Merits:

1.    Its value is based on every item of the series.

2.    It trends itself to algebraic manipulation.

3.    In problems relating to time and rates it gives better results than other averages.

Limitations:

1.    It is not easily understood.

2.    It gives largest weight to smallest items. This is generally not a desirable feature and as such this average is not very useful for the analysis of economic data.

3.    It is difficult to compute.

4.    Its value cannot be computed when there are both positive and negative items in a series or when one or more items are zero.

Because of these limitations the harmonic mean has little practical applications and is not a good representations of a statistical series, unless the phenomenon is such where small items need to be given a very high weight age.

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