The fundamentals of statistics and the limitations of statistics are discussed from their practical and philosophical aspects. In summary results based on statistical methods should be reviewed again and again and corrected if necessary and one should not disregard results which have already been obtained by other basic sciences. In a given goal and the related expectations and opinions it is erroneous to rely completely on the results of a statistical and mathematical calculation. A definitive border between secure knowledge and mere opinion cannot be obtained. Only degrees of certainty exist. The problems of the calculation methods for the perinatal mortality of newborns and their practical conclusions and the question of the relationship between income and number of offspring are used to show that statistical and mathematical methods have their value but cannot be a goal in themselves. It is dangerous to persist in the uncritical belief that each number is equivalent to absolute truth as long as it recorded accurately enough. The ancillary science of statistics does not furnish a general comprehension of the subject matter in natural sciences and the humanities.