For vectors we can use the covariance matrix which contains the variances per variable and the covariances.
Now I want to compare the variances of multiple point clouds. It is hard to compare the covariance matrices directly, so I would like to condense the information to a single variance scalar. (Actually its deviation, i.e. variance's square root.)
What is the typical/classical value to use?
Use the square root of the trace of the covariance matrix (the sum of its diagonal)? Or maybe not use the covariance matrix at all, e.g. computing the average Euclidean distances of each point to the mean of the point-cloud?