Your question is Prove Mean as Centroid. Take a moment with it on the right.
Talk me through your thinking if you like. When you're confident, submit your answer and I'll grade it like a real screen (7/10 or better passes).
Prove why the mean is appropriate as a centroid.
Show that, for observed points and squared Euclidean distance, the arithmetic mean minimizes the total loss over all possible candidate centroids. State the assumptions, establish uniqueness, and explain why a different loss function can produce a different center.
