Society of Actuaries (SOA) PA Practice Exam

What is an Elbow Plot used for in clustering analysis?

1. To determine the number of clusters to use

2. To visualize the distribution of individual data points

3. To assess the potential bias in the clustering algorithm

4. To evaluate the accuracy of the clustering method

The correct answer is: To determine the number of clusters to use

An Elbow Plot is a graphical tool used to determine the optimal number of clusters in a clustering analysis. It is created by plotting the explained variance or the within-cluster sum of squares against the number of clusters. As the number of clusters increases, the variance typically decreases, which is characterized by a slope that diminishes. The "elbow" point on the plot indicates the number of clusters at which adding more clusters yields diminishing returns in terms of variance reduction. This point helps analysts to identify the most appropriate number of clusters to use for meaningful analysis, as it balances model complexity and overfitting. Other options do not accurately describe the function of an Elbow Plot. Visualizing the distribution of individual data points focuses more on understanding data spread and does not directly suggest how many clusters to form. Assessing potential bias in clustering algorithms considers the fairness or representativeness of the clustering decision rather than the determination of cluster quantity. Evaluating the accuracy of the clustering method typically involves different metrics, such as silhouette scores or validation methods, rather than relying on an Elbow Plot.