The important limitations of statistics are:
(1) Statistics laws are true on average. Statistics are aggregates of facts. So single observation is not a statistics, it deals with groups and aggregates only.
(2) Statistical methods are best applicable on quantitative data.
(3) Statistical cannot be applied to heterogeneous data.
(4) It sufficient care is not exercised in collecting, analyzing and interpretation the data, statistical results might be misleading.
(5) Only a person who has an expert knowledge of statistics can handle statistical data efficiently.
(6) Some errors are possible in statistical decisions. Particularly the inferential statistics involves certain errors. We do not know whether an error has been committed or not.
Statistics is an exact science. It is the application of the results that leads to problems.
Perhaps the most commonly encountered limitation of statistics is the misunderstanding that a statistical measure can be used as a measure of the accuracy of a measurement.
Statistics, in general, provide very little information on the intrinsic accuracy of a measurement. Statistics can only provide an estimate of the minimal error that might be in the measurement. The actual error can be much greater than the minimal (statistical) error.
Another way to put it is that statistics measure the variability of a measurement, not the accuracy of a measurement.
Give an introduction to limitation of statistics