The important limitations of statistics are:
(1) Statistics laws are true on average. Statistics are aggregates of facts, so a single observation is not a statistic. Statistics deal with groups and aggregates only.
(2) Statistical methods are best applicable to quantitative data.
(3) Statistics cannot be applied to heterogeneous data.
(4) If sufficient care is not exercised in collecting, analyzing and interpreting 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. In particular, inferential statistics involves certain errors. We do not know whether an error has been committed or not.