Despite the above merits and significance, the diagrammatic representation of data suffers from the following drawbacks :
(i) They are not fit for exhaustive study: Diagrams give only a bird’s-eye-view, or an overall picture of a phenomenon. For a layman, who is not capable of going into the details, this sort of picture is enough. But for a man of special knowledge in statistics, or a researcher who is inclined to make an exhaustive study of the facts and figures, the utility of the diagrams is not much as they are not capable of further analysis and interpretations.
(ii) They are liable to be misused: There are various types of diagrams viz. bars, rectangles, circles, graphs etc, through which data relating to a problem can be represented. But all the types of diagram are not suitable for every type of problem. Some diagrams are appropriate while others look inappropriate for a problem. If a wrong, or inappropriate diagram is chosen, it will lead to a fallacious conclusion, and there will be every likelihood of a wrong diagram being chosen. Hence, it is said that the diagrams are liable to be misused by a statistician.
(iii) They are fit only for comparative study: Diagrams are useful only for comparative study. This requires that there should be a number of diagrams relating to a number of problems which can be studied, and interpreted in a comparative manner. A single diagrams relating to a particular problem carries no meaning and serves no purpose.
(iv) They are liable to be misinterpreted: Diagrams can be easily misinterpreted, and therefore, the statistical data can be misrepresented through them. As such, advertisement, propaganda and electioneering compaign.