Society of Actuaries (SOA) PA Practice Exam

What does the term "horizontal axis" in a dendrogram usually represent?

1. The types of clusters being compared

2. The distance between data points and clusters

3. The categories of variables analyzed

4. The cluster connections at various levels

The correct answer is: The cluster connections at various levels

In a dendrogram, the horizontal axis typically represents the connections between clusters at various levels. This graphical tool is primarily used in hierarchical clustering to visualize the arrangement of the clusters and how they merge at different similarity levels. As you move horizontally along the dendrogram, you can observe how data points or clusters are merged into larger clusters, illustrating the hierarchical structure of the entire dataset. Each connection indicates a merging process, with the length of the horizontal line corresponding to the distance or dissimilarity between the clusters being combined. This provides insight into the clustering relationship, allowing one to assess how closely related different clusters are to one another at specific levels of the hierarchy. The other options might seem plausible at first glance but do not accurately depict what the horizontal axis conveys in a dendrogram. The types of clusters being compared and the categories of variables analyzed are typically represented in legend or label form, not on the axis itself. Additionally, while distance is a crucial aspect of the dendrogram's function, it is not represented on the horizontal axis in the same manner as cluster connections. Overall, understanding the role of the horizontal axis in a dendrogram is essential for interpreting clustering results effectively.