Limitations of Statistics

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Limitations of Statistics pertinent among them are as follows:

There are certain phenomena or concepts where statistics cannot be used. This is because these phenomena or concepts are not amenable to measurement. For example, beauty, intelligence, courage cannot be quantified. Statistics has no place in all such cases where quantification is not possible.
Statistics reveal the average behavior, the normal or the general trend. An application of the ‘average’ concept if applied to an individual or a particular situation may lead to a wrong conclusion and sometimes may be disastrous. For example, one may be misguided when told that the average depth of river from one bank to the other is four feet, when there may be some point’s in-between where its depth is far more than four feet. On this understanding, one may enter those points having greater depth, which may be hazardous.
Since statistics are collected for a particular purpose, such data may not be relevant or useful in other situations or cases. For example, secondary data (i.e., data originally collected by someone else) may not be useful for the other person.
Statistics are not 100 per cent precise as is Mathematics or Accountancy. Those who use statistics should be aware of this limitation.
In statistical surveys, sampling is generally used as it is not physically possible to cover all the units or elements comprising the universe. The results may not be appropriate as far as the universe is concerned. Moreover, different surveys based on the same size of sample but different sample units may yield different results.
At times, association or relationship between two or more variables is studied in statistics, but such a relationship does not indicate cause and effect ‘relationship. It simply shows the similarity or dissimilarity in the movement of the two variables. In such cases, it is the user who has to interpret the results carefully, pointing out the type of relationship obtained.
A major limitation of statistics is that it does not reveal all pertaining to ascertain phenomenon. There is some background information that statistics does not cover. Similarly, there are some other aspects related to the problem on hand, which are also not covered. The user of Statistics has to be well informed and should interpret Statistics keeping in mind all other aspect having relevance on the given problem.