Society of Actuaries (SOA) PA Practice Exam

What type of data structure is produced by hierarchical clustering?

1. A scatter plot of data points

2. A scorecard of clustering accuracy

3. A dendrogram showing data relationships

4. A histogram of cluster sizes

The correct answer is: A dendrogram showing data relationships

Hierarchical clustering is a method of cluster analysis that seeks to build a hierarchy of clusters. The outcome of this method is typically represented as a dendrogram, which is a tree-like diagram that illustrates the arrangement of clusters based on their similarity or distance from one another. In a dendrogram, each leaf node represents an individual data point, while the branches show how these points are merged into clusters at various levels. The height of the branches indicates the distance or dissimilarity between the clusters being joined, allowing you to visualize the gradual merging of data points into larger clusters as the process continues. This hierarchical structure provides clear insights into how closely related the clusters are, making dendrograms a powerful tool for interpreting the results of hierarchical clustering. While other options like scatter plots, scorecards, and histograms provide useful visualizations or metrics, they do not specifically capture the relationships or hierarchy of clusters formed through hierarchical clustering methods. Hence, the dendrogram stands out as the correct representation of the data structure produced by hierarchical clustering.