GIFSQ Tools · Module 16 — Statistics, Experimental Design & Research · Tool 315 of 500
Group observations into clusters with k-means: cluster sizes, centroids and the within-cluster sum of squares that measures how tight the grouping is.
Try sample values — fills the form with the worked example below.
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Within-cluster SS
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Cluster 1 size
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Cluster 2 size
Equation: k-means (Lloyd’s algorithm): assign each point to the nearest centroid, then move each centroid to the mean of its points, and repeat until assignments stop changing. WCSS = Σ over clusters of Σ (point − centroid)².
Method: k-means clustering (MacQueen, 1967; Lloyd’s algorithm). Initial centroids are the first and last observations (and the middle observation for k = 3), so the result is deterministic — the same data always give the same clusters. At most 100 iterations.
Assumptions: the variables are on comparable scales (standardise first if not); clusters are roughly spherical and similar in size; k is chosen by the user, not by the tool.
Limitations: k-means can settle in a local optimum that depends on the starting centroids; with very different scales one variable dominates the distances. The tool does not choose k for you — compare WCSS across k values.
Rounding: centroids to 2 decimal places; WCSS to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Method: k-means clustering (MacQueen, 1967; Lloyd’s algorithm). Initial centroids are the first and last observations (and the middle observation for k = 3), so the result is deterministic — the same data always give the same clusters. At most 100 iterations.
Assumptions: the variables are on comparable scales (standardise first if not); clusters are roughly spherical and similar in size; k is chosen by the user, not by the tool.
Limitations: k-means can settle in a local optimum that depends on the starting centroids; with very different scales one variable dominates the distances. The tool does not choose k for you — compare WCSS across k values.
Rounding: centroids to 2 decimal places; WCSS to 4 decimal places; intermediates unrounded.
This is a calculation aid, not a laboratory report — confirm against your accredited method before citing a value.
Worked example: Points (1,1), (1.5,2), (2,1), (8,8), (8.5,9), (9,8) with k = 2: clusters of 3 and 3, centroids (1.50, 1.33) and (8.50, 8.33), WCSS = 2.3333.
Enter values above to see results.
Compare the WCSS for k = 1, 2 and 3: a sharp drop (the elbow) suggests the right number of clusters. Tool 315 of 500 — GIFSQ
