If the Between-Clusters Sum of Squares relative to the total variance is high, what does this imply about cluster separation?

If the Between-Clusters Sum of Squares relative to the total variance is high, what does this imply about cluster separation?

• A. Poor separation
• B. No information
• C. Moderate separation
• D. Better separation

Answer: (D)

The main idea is that the Between-Clusters Sum of Squares relative to the total variance shows how much of the data’s variability is due to differences between cluster centers. A high BCSS relative to total variance means the cluster centers are far apart compared with how spread out the points are within each cluster, so most of the variance comes from the separation between clusters. That indicates clearer, better separation of the clusters. If the ratio were low, it would suggest little separation, with points within clusters dominating the variance.

The main idea is that the Between-Clusters Sum of Squares relative to the total variance shows how much of the data’s variability is due to differences between cluster centers. A high BCSS relative to total variance means the cluster centers are far apart compared with how spread out the points are within each cluster, so most of the variance comes from the separation between clusters. That indicates clearer, better separation of the clusters. If the ratio were low, it would suggest little separation, with points within clusters dominating the variance.