[rm999]

I almost completely agree with you. I often tell people that statistics is the study of compressing information in useful ways. That said, scalar statistics can be very useful if the compression is 'correct'. For example, if you have an a priori reason to believe a distribution will be gaussian (a very common situation, and an assumption that basically allowed statistics to be grow to where it is today), mean and variance will fully describe the distribution. Many other common distributions can be fully described by a small number of parameters.