merits_and_demerits

Merits and Demerits of Mean, Median, Mode

Merits of Mean

It is rigidly defined, easy to understand and calculate
It takes all values into consideration giving weight to all
It is used in the computation of other statistical measures
It least affected by fluctuation of sampling
It is a good basis for comparison

Demerits of Mean

It cannot be determined by inspection, cannot be located graphically and cannot be used in the study of qualitative phenomena
It can be significantly impacted by extreme values
It cannot be calculated if the distribution has open-ended classes
It cannot be calculated if a single observation is missing
Arithmetic mean can be a figure that does not exist in the series at all
It is not suitable in case of extremely asymmetrical distribution

Merits of Median

It is rigidly defined, easy to understand and calculate
It is not influenced by extreme values
It can be computed for distributions that have open-end classes
It can be determined by inspection and located graphically
It can be calculated even if some of the extreme values are not available

Demerits of Median

It may not be close to the centre in many cases
It does not consider all the items of the series
It is significantly impacted by fluctuations of sampling
It is not suitable for further algebraic treatment
It is unsuitable if it is desired to give greater importance to large or small values
It is a figure that is not in the series if the number of observations 'n' is even

Merits of Mode

It is easy to understand
It is not influenced by items on the extremes
It can be located even if the class intervals are of unequal magnitude
It can be computed for distributions which have open-ended classes
It can be determined by inspection and can be located graphically

Demerits of Mode

Calculation of mode does not consider all the items of the series
It is not rigidly defined and hence ambiguous when two or more observations are repeated same number of times
It is not capable of further mathematical treatment
It is severely impacted by fluctuations of samplings
It is considerably influenced by the choice of grouping

Relationship between Mean, Median and Mode

Mode touches the peak of the curve indicating maximum frequency. Median divides the area of the curve in two equal halves and mean is the centre of gravity. The following points list the relationship between them:

In a distribution, the relative position of Mean, Median and Mode depend upon the skewness of the distribution. If the distribution is exactly symmetrical then

Mean = Median = Mode

If the distribution is positively skewed, the mode will be lesser than the median, which in turn will be lower then the arithmetic mean.
In case of negatively skewed distribution, the mode will be greater then the median which in turn will be greater than the Arithmetic Mean.
In a given distribution, if all the observations are positive,

AM > GM > HM

With a distribution of moderate skewness, median tends to be approximately rd as far away from the mean as from the mode.