Why is it good to serve the average quality of an object? We benchmark a machine on a nymber of tests. It passes eacg test in some time. Why RMS is used to find out the best machine? It seems that I have found a good illustration.
The RMS can be visualized. Just draw a multidimentional space with number of dimentions equal to the number of attributes. (every tests measures some attribute, some quality). Some objects are better in one test, other in another (we imply that larger the attribute the better). Which one has better overall indices? The one with longest radius-vector! An object is a multidimentional space (of attributes) is a vector! RMS finds out the length of the vector, the norm of the object.