Merits and Demerits of All types of Mean

Merits and Demerits of Arithmetic Mean

Merits of Arithmetic Mean:

• It is rigidly defined.
• It is easy to calculate and simple to follow.
• It is based on all the observations.
• It is determined for almost every kind of data.
• It is finite and not indefinite.
• It is readily put to algebraic treatment.
• It is least affected by fluctuations of sampling.

Demerits of Arithmetic Mean:

• The arithmetic mean is highly affected by extreme values.
• It cannot average the ratios and percentages properly.
• It is not an appropriate average for highly skewed distributions.
• It cannot be computed accurately if any item is missing.
• The mean sometimes does not coincide with any of the observed value.                           

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Merits and Demerits of Geometric Mean

Merits of Geometric Mean:

• It is rigidly defined and its value is a precise figure.
• It is based on all observations.
• It is capable of further algebraic treatment.
• It is not much affected by fluctuation of sampling.
• It is not affected by extreme values.

Demerits of Geometric Mean:

• It cannot be calculated if any of the observation is zero or negative.
• Its calculation is rather difficult.
• It is not easy to understand.
• It may not coincide with any of the abservations.

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Merits and Demerits of Harmonic Mean

Merits of Harmonic Mean:

• It is based on all observations.
• It not much affected by the fluctuation of sampling.
• It is capable of algebraic treatment.
• It is an appropriate average for averaging ratios and rates.
• It does not give much weight to the large items

Demerits of Harmonic Mean:

• Its calculation is difficult.
• It gives high weight-age to the small items.
• It cannot be calculated if any one of the items is zero.
• It is usually a value which does not exist in the given data.

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Merits and Demerits of Median

Merits of Median :

·         It is easy to compute and understand.

·          It is well defined an ideal average should be.

·          It can also be computed in case of frequency distribution with open ended classes.

·          It is not affected by extreme values and also interdependent of range or dispersion of the data.

·          It can be determined graphically.

·          It is proper average for qualitative data where items are not measured but are scored.

Demerits of Median :

·         For computing median data needs to be arranged in ascending or descending order.

·          It is not based on all the observations of the data.

·         It can not be given further algebraic treatment.

·         It is affected by fluctuation of sampling.

·          It is not accurate when the data is not large.

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Merits and Demerits of Mode

Merits of Mode:

• It is easy to understand and simple to calculate.
• It is not affected by extreme large or small values.
• It can be located only by inspection in ungrouped data and discrete frequency distribution.
• It can be useful for qualitative data.
• It can be computed in open-end frequency table.
• It can be located graphically.

Demerits of Mode:

• It is not well defined.
• It is not based on all the values.
• It is stable for large values and it will not be well defined if the data consists of small number of values.
• It is not capable of further mathematical treatment.
• Sometimes, the data having one or more than one mode and sometimes the data having no mode at all.

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