diff --git a/kmeans/algorithms.py b/kmeans/algorithms.py
index dfe89a2..0702ea7 100644
--- a/kmeans/algorithms.py
+++ b/kmeans/algorithms.py
@@ -26,9 +26,13 @@ def mean_movement(clusters: List[Cluster]) -> float:
     return highest_movement
 
 
-def unweighted_k_means(points: List[Point], k: int, d: float = 0.001) -> List[Cluster]:
+def k_means(points: List[Point], k: int, d: float = 0.001) -> List[Cluster]:
     """
-    Runs Lloyd's Algorithm for k-means clustering without weights.
+    Runs Lloyd's Algorithm for k-means clustering.
+
+    If no weights are added (that is, all point weights are 1) the mean is
+    found using the arithmetic mean. If there are weights, the mean will be
+    a weighted mean of the points.
 
     @param points The list of points to cluster.
     @param k The number of clusters.
@@ -75,13 +79,19 @@ def unweighted_k_means(points: List[Point], k: int, d: float = 0.001) -> List[Cl
         for cluster in clusters:
             # Update the mean with the new points
             if cluster.points is not None:
-                xs = [p.x for p in cluster.points]
-                ys = [p.y for p in cluster.points]
+                # When all weights are 1 the sum of these lists will be
+                # the exact same thing as the standard arithmetic mean.
+                xs = [p.x * p.weight for p in cluster.points]
+                ys = [p.y * p.weight for p in cluster.points]
+
+                # When all weights are 1, the sum of this list is
+                # exactly the length of the list.
+                weights = [p.weight for p in cluster.points]
 
                 # Averaging the xs and ys will give us the mean point
                 # of our cluster.
-                new_x = sum(xs) / len(xs)
-                new_y = sum(ys) / len(ys)
+                new_x = sum(xs) / sum(weights)
+                new_y = sum(ys) / sum(weights)
 
                 new_mean = Point(new_x, new_y)