In this note we first show that the centroid (or centre of gravity) gives in value a ( σ + 1 ) -approximation to any continuous single facility minisum location problem for any gauge with asymmetry measure σ, and thus a 2-approximate solution for any norm. On the other hand for any gauge the true minimum point (the 1-median) remains within a bounded set whenever a fixed proportion of less than half of the total weight of the destination points is moved to any other positions. It follows that the distance between the centroid and the 1-median may be arbitrary close to half the diameter of the destination set. 
How bad can the centroid be?