Question 6
Content Domain 2: Exploratory Data AnalysisA data scientist runs k-means with several values of k and plots the within-cluster variation against the number of clusters. Which technique is being used to help choose an appropriate cluster count?
Correct answer: B
Explanation
An elbow plot helps select a reasonable number of clusters by comparing how much within-cluster variation decreases as cluster count increases. Cluster analysis diagnostics should match the specific decision being made, such as choosing k versus inspecting hierarchy. — Perform cluster analysis (for example, hierarchical, diagnosis, elbow plot, cluster size).
Why each option is right or wrong
A. Hierarchical clustering
Hierarchical clustering organizes observations into nested groups rather than plotting variation across multiple k values.
B. Elbow plot
The scenario describes plotting within-cluster variation against the number of clusters to identify the point where additional clusters yield diminishing improvement. In cluster analysis, that diagnostic is an elbow plot, used specifically to help choose an appropriate cluster count.
C. Cluster size review
Cluster size review examines how many observations fall into each cluster, not the change in variation as k increases.
D. Diagnosis of hierarchy depth
Hierarchy depth applies to hierarchical methods, not to selecting k from a plot of within-cluster variation.