Each document is a K dimensional vector. Similarly, the mean of the cluster is a k dimensional vector where each component is an average of the corresponding component for each of the m documents. A document error is the square root of the sum of the squared differences of each of its k components with each of the  k components of the  mean of the cluster. The RMSSTD is a an error for the entire cluster so to incorporate all documents from the cluster in this err caculation, it becomes the sum of the squared differences for every component of every document. There are m*k components to sum over in this case.   Russ ... View more