In k-Means, what are the centers of clusters called?

• A. Means
• B. Coordinates
• C. Medians
• D. Centroids

Answer: (D)

In k-means, the center of each cluster is the centroid. The centroid is the average position of all points assigned to that cluster: you compute the mean for each feature across those points, giving a multi-dimensional center that lies in the same feature space. This choice aligns with the objective of minimizing the sum of squared distances within clusters; in Euclidean space, the point that minimizes this sum is exactly the arithmetic mean along every dimension, so the centroid is the optimal center after each assignment step. For example, with points at (1,2) and (3,4), the centroid is (2,3). The term coordinates just describe where this center sits, while medians would minimize a different loss function (L1 distance). The standard term used for the center in k-means is centroid, reflecting its interpretation as the multi-dimensional mean.