Cluster Analysis Calculator

K-means clustering is an unsupervised machine learning algorithm that partitions a dataset into k groups (clusters) by minimizing the total within-cluster sum of squared distances from each point to its cluster centroid. Points in the same cluster are more similar to each other than to points in other clusters.

If your variables are measured on very different scales (e.g. age in years vs. income in thousands), variables with larger numeric ranges will dominate the distance calculations unfairly. Standardizing (z-score normalization) puts all variables on the same scale so each contributes equally to the clustering.

A common approach is the elbow method — run k-means for different values of k and plot the total SSE. The 'elbow' point where SSE stops decreasing steeply suggests a good k. Domain knowledge and interpretability should also guide your choice.

K-means initializes centroids randomly, so different runs can converge to different local minima. The 'Repeats' setting reruns the algorithm multiple times with different random starts and keeps the result with the lowest total SSE, making the solution more stable.

SSE measures the total squared distance between each data point and the centroid of its assigned cluster. A lower SSE means the clusters are tighter and more compact. It is the main objective function that k-means minimizes.

Enter numeric values separated by commas or new lines. For example: 2, 5, 10, 11, 20. Non-numeric characters and empty cells are automatically ignored. This calculator works on a single numeric variable; for multi-variable clustering, separate x,y pairs per line.

A centroid is the mean (average) of all data points assigned to a cluster. In each iteration, k-means recalculates centroids after reassigning points, repeating until assignments no longer change (convergence).

Yes. Points that are very far from their assigned centroid relative to the typical within-cluster spread may be considered outliers. A high SSE contribution from a single point is a strong signal that it doesn't fit well into any cluster.