In spite of its important functions, statistics has its limitations too. These limitations should be kept in mind while using the various statistical methods. Now, we shall discuss some of the limitations of statistics.
1.) Statistics deals only with the quantitative characteristics: Statistics deals with facts which are expressed in numerical terms. Therefore, those phenomena that cannot be described in numerical terms do not fall under the scope of statistics. Beauty, colour of eyes, intelligence, etc., are qualitative characteristics and hence cannot be studied directly. These characteristics can be studied only indirectly, by expressing them numerically after assigning particular scores. For example, we can study the level of intelligence of a group of persons by using intelligence quotients (I.Qs).
2.) Statistics does not deal with individuals: Since statistics deals with aggregate of facts, a single and isolated figure cannot be regarded as statistics. For example, the height of one individual is not of much relevance but the average height of a group of people is relevant from statistical point or view. In this context, you may recall the definition given by Secrist here.
3.) Statistical laws are not exact: Unlike the laws of natural sciences, statistical laws are not exact. They are true under certain conditions and always some chance factor is associated with them for being true. Therefore, conclusions based on them are only approximate and not exact. They cannot be applied universally. Laws of pure sciences like Physics and Chemistry are universal in their application.
4.) Statistical results are true only on an average: Statistical methods reveal only the average behaviour of a phenomenon. The average income of employees of a company will, therefore, not throw much light on the income of a specific individual. They are therefore, useful [or studying a general appraisal of a phenomenon.
5.) Statistics is only one of the methods of studying a problem: A problem can be studied by several methods. Statistical methods arc only one of them. Under all circumstances, statistical tools do not provide the best solution. Quite often it is necessary to consider a problem in the light of social considerations like culture, region, etc. Therefore, statistical conclusions need to be supplemented by other evidences.
6.) Statistics can be misused: The various statistical methods have their own limitations. If used without caution they are subject to wrong conclusions. So one of the main limitations of statistics is that, if put into wrong hands, it can be misused. This misuse can be, at times, accidental or intentional. Many government agencies and research organisations are tempted to use statistics to misrepresent the facts to prove their own point of view. Suppose you are told that during a year the number of car accidents in a city by women drivers is 10 while those committed by men drivers is 40. On the basis of this information, you may conclude that women are safe drivers. If you conclude like that you are misinterpreting the information. You must know the total number of drivers of both types before you could arrive at a correct conclusion.
