In the k-means algorithm, data points are assigned to the cluster with which of the following?

• A. Nearest Mean
• B. Nearest Median
• C. Nearest Mode
• D. Nearest Range

Answer: (A)

K-means assigns each data point to the cluster whose center, or centroid, is closest in terms of distance. The centers are the means of the points currently in each cluster, and the distance used is usually Euclidean distance. The reason this works is that, for a given cluster, the mean minimizes the sum of squared distances from all its points to that center. So choosing the nearest mean effectively groups points by minimizing within-cluster variance.

After assigning points, the centers are recomputed as the average of the points in each cluster, and the process repeats until convergence. The other options—nearest median, nearest mode, or nearest range—pertain to different methods or data types (for example, k-medians uses medians), but they do not define the standard k-means assignment rule.