It is absolutely true that statistical methods are not the substitute for common sense. Statistical data should not be believed blindly as they can be misinterpreted or misused. The statistical data may involve personal biasedness or may be subjected to manipulations for one’s own selfish motives.
Statistical data and methods are also subject to the errors committed by an investigator while surveying and collecting data. Thus, one should use his/her common sense while working with the statistical methods.
A classic example exhibiting this concept is a statistician wanted to cross a river with his family but did not know how to swim. He knew the average depth of the river to be 125 cm. His height was 175 cm, that of his wife was 152 cm and his two children measured 120 cm and 90 cm respectively, in height.
He calculated the average height of his family and found it to be around 134 cm. He analysed that the average depth of the river was less than the average height of his family and concluded that they all could cross the river safely on foot. This resulted in drowning of his children. This example proves that common sense must supersede statistical methods.