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.