Measure natural groupings from one-dimensional datasets with helpful summaries. Review centroids, ranges, compactness, and balance. Visualize clusters and export polished results with confidence today.
Enter one-dimensional numeric data using commas, spaces, or new lines.
cj = (Σ xi) / nj
Each centroid equals the average of values inside that cluster.
Distance = (xi - cj)²
Each point joins the nearest centroid using squared distance.
WCSS = Σ Σ (xi - cj)²
Lower WCSS usually means tighter groups around each centroid.
BSS = TSS - WCSS
Higher BSS suggests stronger separation across cluster centers.
Separation Ratio = (BSS / TSS) × 100
This percentage shows how much spread is explained by grouping.
This sample demonstrates a dataset with three clear value groups.
| Sample Dataset | Suggested K | Expected Cluster Pattern | Interpretation |
|---|---|---|---|
| 4, 5, 6, 7, 19, 21, 23, 24, 45, 46, 48, 50 | 3 | Low, middle, and high groups | Useful for spotting natural concentration zones. |
| 11, 12, 12, 13, 29, 30, 31, 49, 50, 52 | 3 | Three compact centroids | Shows balanced clusters with visible separation. |
| 3, 4, 5, 15, 16, 17, 27, 28, 29 | 3 | Evenly spaced bands | Good for teaching centroid-based grouping. |
It groups one-dimensional numeric values into clusters using a centroid-based method. It also reports spread, compactness, separation, and point-to-centroid assignments for deeper statistical review.
A centroid is the average value inside a cluster. It acts as the cluster center and helps determine which points belong together during each iteration.
WCSS measures how tightly points sit around their assigned centroid. Lower values usually indicate more compact clusters and reduced internal variation.
Start with a small number, then compare separation and compactness across runs. The best choice often balances meaningful grouping with low internal spread.
Yes. The calculator accepts integers, decimals, and negative values. Separate entries with commas, spaces, or new lines.
No. This version is designed for one-dimensional datasets. It is ideal for learning, quick reviews, and simple numeric segmentation tasks.
It estimates how much total variation is explained by the cluster structure. Higher percentages generally suggest stronger distinctions between groups.
CSV files help with spreadsheets and downstream analysis. PDF files help with reporting, documentation, and sharing a clean summary with others.
This calculator uses one-dimensional k-means style clustering.
Population variance is used throughout the summary tables.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.