Statistics is a very useful branch of study finding applications in diverse fields ranging from physics and chemistry to economics and psychology. But this should not be understood to mean that statistics provides a solution to every problem.

Therefore it becomes important to understand the limitations of statistics as a tool for study. We now list 5 important limitations of statistics as a field of study.

**1. Statistics is not suited to the study of qualitative phenomenon**

Statistics being a science dealing with a set of numerical data, is applicable to the study of only those subjects of inquiry that are capable of quantitative measurement.

As such qualitative phenomena like honesty, poverty, culture, etc., which cannot be expressed numerically, are not capable of direct statistical analysis.

However, statistical techniques may be applied indirectly by first reducing the qualitative expressions to precise quantitative terms. For example, the intelligence of a group of candidates can be studied on the basis of their scores on a certain test.

**2. Statistics does not study individuals**

Statistics deals with an aggregate of objects and does not give any specific recognition to the individual items of a series. Individual items, taken separately, do not constitute statistical data and are meaningless for any statistical inquiry.

For example, the individual figures of agricultural production, industrial output, or national income of a country for a particular year are meaningless unless, to facilitate comparison, similar figures of other countries or of the same country for different years are given. Hence, statistical analysis is suited to only those problems where group characteristics are to be studied.

**3. Statistical laws are not exact. They are only true on average.**

Unlike the laws of physical and natural sciences, statistical laws are only approximations and not exact. On the basis of statistical analysis, we can talk only in terms of probability and chance and not in terms of certainty.

Statistical conclusions are not universally true – they are true only on average. For example, let us consider the statement: “It has been found that 20% of a certain surgical operation by a particular doctor is successful.” The statement does not imply that if the doctor is to operate on 5 persons on any day and four of the operations have proved fatal, the fifth must be a success.

It may happen that the fifth man also dies of the operation or it may also happen that of the five operations on any day, 2 or 3 or even more may be successful. By the statement we mean that as the number of operations becomes larger and larger we should expect, on average, 20 % of the operations to be successful.

**4. Statistics is liable to be misused**

Perhaps the most important limitation of Statistics is that it must be used by experts. As the saying goes, “Statistical methods are the most dangerous tools in the hands of the non-experts.”

The use of statistical tools by inexperienced persons might lead to very fallacious conclusions. The requirement of experience for judicious use of statistical methods restricts their use to experts only and limits the chances of the mass popularity of this useful and important science.

**5. Statistics is not the whole answer to every problem**

Statistical tools do not provide a complete picture of every problem. It is often necessary to look at the problem in the light of a cultural perspective in order to come up with a holistic solution to some problems. Therefore statistical reasoning should be supplemented by other modes of thinking.