Calculation Results
Cluster Summary
Centroids
Point-Level Distances
Elbow Analysis
Substituted Formula and Steps
Formula Used
WCSS = Σj=1K Σxᵢ ∈ Cⱼ ‖xᵢ − μⱼ‖²
- K is the number of clusters.
- Cⱼ is the set of points in cluster j.
- xᵢ is an observation vector.
- μⱼ is the centroid of cluster j.
Lower WCSS means points are closer to their centroids. WCSS normally decreases as K increases. Use elbow evidence with other validation metrics.
How to Use
- Paste data or upload a CSV file.
- Parse the data and select numeric features.
- Choose assigned, centroid, K-means, elbow, or single mode.
- Configure scaling, missing values, weights, and clustering controls.
- Calculate and inspect WCSS, centroids, tables, charts, and exports.
Example Data
| Point | Feature 1 | Feature 2 | Cluster |
|---|---|---|---|
| A | 1 | 2 | 1 |
| B | 2 | 2 | 1 |
| C | 8 | 7 | 2 |
| D | 9 | 8 | 2 |
Frequently Asked Questions
What does WCSS measure?
It measures total squared distance from points to assigned centroids.
Is a lower WCSS always better?
Lower values indicate tighter clusters, but larger K automatically lowers WCSS.
Why should features be scaled?
Large-scale features can dominate squared Euclidean distances and cluster assignments.
What is the elbow method?
It compares WCSS across K values and seeks diminishing improvement.
Can WCSS compare different datasets?
Direct comparison is risky unless dimensions, scaling, and sample sizes match.
What is between-cluster sum of squares?
It is total variation minus within-cluster variation for the selected partition.
How are manual centroids used?
Each point is assigned to its nearest supplied centroid before summation.
What happens with empty clusters?
The chosen strategy reseeds, preserves, or replaces an empty centroid.
Should WCSS be used alone?
No. Combine it with silhouette analysis, stability checks, and domain knowledge.