Elementary Statistics (1+1)

6.2.2 Merits and Demerits of Arithmetic Mean

Merits

i) It is rigidly defined

ii) It is easy to understand and easy to calculate

iii) It is based upon all the observations

iv) It is amenable to algebraic treatment. The mean of the composite series in terms of the means and sizes of the component series is given by

v) Of all the averages, arithmetic mean is affected least by fluctuations of

sampling. This property is sometimes described by saying that mean is a stable

average.

Thus, we see that arithmetic mean satisfies all the properties laid down by Prof. Yule for an ideal average.

Demerits

i) Arithmetic mean is affected very much by extreme values. In case of extreme items, arithmetic mean gives a distorted picture of the distribution and no longer remains representative of the distribution.

ii) Arithmetic mean may lead to wrong conclusions if the details of the data from which it is computed are not given. Let us consider the following marks obtained by two students A and B in three tests, viz, terminal test, half-yearly examination and annual examination respectively.

Marks in : I Test II Test III Test Average marks

A 50% 60% 70%

B 70% 60% 50%

Thus average marks obtained by each of the two students at the end of the year are 60%. If we are given the average marks alone we conclude that the level of intelligence of both the students at the end of the year is same. This is a fallacious conclusion since we find from the data that student A has improved consistently while student B has deteriorated consistently.

iii) Arithmetic mean cannot be calculated if the extreme class is open, e.g. below 10 or above 70. Moreover, even if a single observation is missing mean cannot be calculated.