CHOICE OF SUITABLE AVERAGE

we have discussed various averages viz., mean, geometric mean, median, partition values and mode etc.  You have studied merits, demerits, and specific uses of each of these averages separately.  Now, we should know how to make choice of a suitable average for a given purpose.  Examining from the point of view of essential qualities of a good measure of central tendency, arithmetic qualities.  Given the situation, however, the choice of a suitable average poses a problem.  If the choice is not proper, the conclusions will not be much dependable.  With an improper choice of an average, the comparative scene that emerges will be far from reality.  Therefore, while making the choice of an average, you should keep in mind the following aspects.

1) The Purpose:  The choice is to be made in accordance with the purpose that an average is designed to serve.  If the purpose is to give all the items of the series an equal importance, arithmetic mean will be a proper average.  If the purpose is to find the most common or most fashionable item, the mode will be a suitable average.  If the purpose is to locate a position of an item in relation to other items, it would be the median that serves the purpose.  When small items are to be given a little more importance than big items, the choice falls on geometric mean.  If sufficiently greater weights are to be assigned to smaller values, harmonic mean should be used.

2) Nature and the Form of the data Set:  If the distributions are skewed, mode or mean will be preferred.  For an open-ended distribution, again mode or median would be more suitable.  In case of j-shaped or reverse j-shaped distribution i.e., which highly deviate from symmetry, the median is the most arithmetic mean will be an appropriate average.  Price distribution and income distribution are two examples of it.  If the data is evenly spread out and does not display wide variations, the arithmetic mean will be an appropriate average.  Average cost of production is an example if it.  When the ratios or percentages are to be averaged, geometric mean is the most appropriate measures.  The data set in which the value of a variable is compared with another variable which is constant, harmonic mean is the most suitable average.  Examples are varying speed with constant distance, varying quantities bought per rupee, etc.

3) Amenability to further Algebraic Treatment:  If an average is to be used for further algebraic treatment, arithmetic mean is considered to be the best as it is very widely used.

4) Qualitative Phenomena:  For the characteristics which are qualitative in nature such as honesty, beauty, intelligence, etc., median seems to be proper average.

5) Special Purpose:  For calculating trend in time-series analysis, the moving average would be most suitable average.  Though the above considerations act as a guiding principle in making a choice of a suitable average, in many cases it is arbitrary.  If the higher value is required to prove the hypothesis, it is tempting to use the measure which give the higher value.  Since we can select the measures of central tendency to sit our fancy, there is a possibility of selecting the average which produces the result we want.  When use unscrupulously or incompetently, the user is at fault not the tool.

Mayank Rai

Hi, My name is Mayank Rai. I found that Blogging is an easiest way to share your knowledge with everyone & learn something new from there. facebook whatsapp telegram