The best measure of central tendency, usually, is the AM. It is rigidly defined, based on
all the observations, easy to comprehend, simple to calculate and amenable to
mathematical properties. However, AM has one drawback in the sense that it is very
much affected by sampling fluctuations. In case of frequency distribution, mean cannot
be advocated for open-end classification.
Median is also rigidly defined and easy to comprehend and compute. But median is not
based on all the observation and does not allow itself to mathematical treatment.
However, median is not much affected by sampling fluctuation and it is the most
appropriate measure of central tendency for an open-end classification.
Mode is the most popular measure of central tendency, there are cases when mode
remains undefined. Unlike mean, it has no mathematical property. Mode is also affected
by sampling fluctuations.
Relationship between Mean, Median and Mode
Mean – Mode = 3(Mean – Median)
Mode = 3 Median – 2 Mean
Relation between AM, GM, and HM
AM ≥GM ≥HM
GM and HM, like AM, possess some mathematical properties. They are rigidly defined
and based on all the observations. But they are difficult to comprehend and compute and,
as such, have limited applications for the computation of average rates and ratios and
such like things.