In any set of data, though the values of the observations are not equal, a general tendency of these observations to cluster around a particular point or level is noticed. In this situation, it may be necessary to distinguish each group of observations by such a level or point (value), which is referred to as the central tendency of that group.
This single value for each group of observations serves as a representative of that group. This level or point may vary from group to group and is known as the average. For example, the average haemoglobin levels of people of two different age groups vary. Though individual values may overlap, the two distributions have different central positions and therefore differ in their characteristic of the location.
Limitations of Averages in Statistics:
In spite of its very wide applications in statistical analysis, the averages have the following limitations :
- Since the average is a single numerical figure representing the characteristics of a given distribution, proper care should be taken in interpreting its value otherwise it might lead to very misleading conclusions.
- A proper and judicious choice of an average for a particular problem is very important. A wrong choice of the average might give wrong and fallacious conclusions.
- An average fails to give the complete picture of a distribution. We might come across a number of distributions having the same average but differing widely in their structure and constitution. To form a complete idea about the distribution, the measures of central tendency are to be supplemented by some more measures such as dispersion, skewness, and kurtosis.
- In certain types of distributions like U-shaped or J-shaped distributions, an average (which is only a single point of concentration) fails to represent the entire series.
- Sometimes an average might give very absurd results. For instance, the average number of people in a family might come out in fractions which are obviously absurd. For example, if the birthrate of a particular country is 2.2 children per woman it does not mean that a woman gives birth to 2.2 children which is clearly absurd.
References:
Business Statistics – S.C Gupta
