FRM Part I · FRM Exam Part I · Machine Learning and Prediction
Three clusters from a K-means run on one-dimensional data have these members: A = {2, 4}, B = {10, 12, 14}, C = {20}. Using each cluster's own mean as its centroid, what is the total within-cluster sum of squares (inertia)?
The inertia is 10. Cluster A has mean 3 and contributes 2, cluster B has mean 12 and contributes 8, and the single-point cluster C contributes 0. Summing squared deviations from each cluster mean gives 2 + 8 + 0 = 10.
- A8
- B10Correct
- C12
- D14
Explanation
A: mean 3, squares 1+1 = 2. B: mean 12, squares 4+0+4 = 8. C: single point, 0. Total = 2+8+0 = 10. Answer 8 omits cluster A, and 12 wrongly treats A's deviations as 4.
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