Despite the usefulness of statistics in many fields, impression should not be carried that statistics
are like magical devices which always provide the correct solution to problems. Unless the data are properly collected and critically interpreted there is every likelihood of drawing wrong conclusions. Therefore, it is also necessary to know the limitations and the possible misuses of
statistics. The following are the important limitations of the science of statistics:

1. Statistics does not deal with individual measurements.

Since statistics deals with aggregates of facts, the study of individual measurements lies outside the scope of statistics. Data are statistical when they relate to measurement of masses, not statistical when they relate to an individual item or event as a separate entity. For example, the wage earned by an individual worker at any one time taken by itself is not a statistical datum. But the wages of workers of a factory can be used statistically. Similarly, the marks obtained by one student of a class or his height are not the subject-matter of the study of statistics but the average marks of the average height has statistical relevance.

2. Statistics deals only with quantitative characteristics.

Statistics are numerical statements of facts. Such characteristics as cannot be expressed in numbers are incapable of statistical analysis. Thus, qualitative characteristics like honesty, efficiency, intelligence, blindness and deafness cannot be studied directly. However, it may be possible to analyse such problems statistically by expressing them numerically. For example, we may study the intelligence of boys on the basis of the marks obtained by them in an examination.

3. Statistical results are true only on an average.

The conclusions obtained statistically are not universally true; they are true only under certain conditions. This is because statistics as a sciences is less exact as compared to natural sciences.

4. Statistics is only one of the methods of studying a problem.

Statistical tools do not provide the best solution under all circumstance. Very often, it is necessary to consider a problem in the light of a country’s culture, religion and philosophy. Statistics cannot be of much help in studying such problems. Hence statistical conclusion should be supplemented by other evidences.

5. Statistics can be misused.

The greatest limitations of statistics is that it is liable to be misused. The misuse of statistics may arise because of several reasons. For example, if statistical conclusions are based on incomplete information, one may arrive at fallacious conclusions. Thus the argument that drinking beer is bad for longevity because 99% of the persons who take beer die before the age of 100 years is statistically defective, since we are not told what percentage of persons who do not drink beer die before reaching that age. Statistics are like clay and they can be moulded in any manner so as to establish right or wrong conclusions. In this context, W.I. King pointed out “one of the shortcomings of statistics is that they do not bear on their  face the label of their quality.” Moreover, any Tom, Dick and Harry cannot deal with statistics. It requires experience and skill to draw sensible conclusions from the data; otherwise, there is every likelihood of wrong interpretation. The very fact that is may lead to fallacious conclusions in the hands of inexperienced people limits the possibility of mass popularity of such a useful science. Also, statistics cannot be used to full advantage in the absence of proper understanding of the subject to which it is applied.

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