Demerits and merits of the measures of central tendency

The arithmetic mean or a.m

Merits

i.  It employs all the observations given

ii. This is a very useful statistic in terms of applications. This has some applications in business management for illustration as: hypothesis testing, quality control and so on.

iii. This is the best representative of a described set of data if such data was acquired from a normal population

iv. The arithmetic mean can be determined accurately by using mathematical formulas

Demerits

i. If the data is not drawn from a 'general population, then the arithmetic mean may provide a wrong impression about the population

ii. In some situations, the arithmetic mean may provide unrealistic values especially when dealing along with discrete variables for illustration as: when working out the average no. of children in a number of families. This may be found that the average is 4.4 which is un-realistic in human beings