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:

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.