I have a set of measurement points obtained from a sensor and each data point has a standard deviation (which is assumed to be the same for all the points). Clustering is applied and the center of the cluster is calculated by taking the average of the x and y positions of all the points within a cluster. The clustersize (R) of each cluster is the same but the number of points within a cluster is varying.
The question is how to calculate the standard deviation for the center of the cluster by taking into account the standard deviation of each individual point within that cluster?