How to make standard deviation meaningful

Variability is a somewhat difficult concept. There is no internal relation in it which gives you insight into the concept of standard deviation at an intuitive level. Some relations that are very important to standard deviation are discussed. They relate standard deviation to mean and other notions at an abstract level. In a broader context of "statistics (mathematics ) as a tool to communicate" they loose their fascination. Maybe we will overcome this problem by techniques of exploratory data analysis and thus cope with the idea of variability more successful in the future.