The word statistics is used both in plural as well as in singular sense. In plural sense, statistics means numeric facts which can be used to draw conclusions and in singular sense, it means the statistical methods with the help of which statistical information is used to treat and draw conclusions from them.
There are following limitations of statistics :
Sometimes, when data are not properly collected 1 then there is likelihood to draw wrong conclusions.
Therefore, it is necessary to know the limitations of statistics.
(i) Statistics does not study about individuals : Statistics are expressed in facts. It does not study individuals. For example, there are five students in a class. Statistics only tells the average marks obtained in class not how many marks are obtained by every student in the class.
(ii) It does not study the qualitative aspect of problem : The most important condition of statistical study is that subject of investigation and inquiry should be capable of being qualitatively measured. For example, honesty, poverty, etc.
(iii) Statistics can be misused: The result obtained can be manipulated accordingly to one's own interest and such manipulated results can mislead the community.
(iv) Statistical results lack mathematical accuracy: The results drawn from statistical analysis are normally in approximates. As the satistical analysis is based on observation of mass data, number of inaccuracies may be present and it is difficult to rectify them.
(v) Uniformity and homogeneity of data : It is essential that data must have the quality of uniformity and homogeneity. Heterogeneous data are not comparable. For example, it would be meaningless to compare the heights of men with heights of trees because these figures are of heterogeneous character.