I have a dataset of vectors and need to find the sum of squares or variance based on the euclidean distance between the vectors.

I can do this by finding the "average" vector (by calculating the average components of the vectors) and then summing up the squared euclidean distance between each vector and the average vector.

Is there a way to do this on the "fly" without calculating the average vector? I am familiar with the short cut method for finding the variance of a one-dimensional datasets and would like to find something similar for vectors.

Any help is greatly appreciated.