Which statements about hierarchical clustering are true?

The statement indicating that the dendrogram can show various cluster numbers is accurate because one of the key features of hierarchical clustering is its ability to produce a dendrogram, a tree-like diagram that illustrates the arrangement of clusters at different levels of granularity. When you cut the dendrogram at different heights, you can create various numbers of clusters based on your specific needs or interpretations of the data. This flexibility allows analysts to choose a meaningful number of clusters depending on the context of the analysis.

In contrast, hierarchical clustering is sensitive to outliers since they can significantly alter the distance calculations used in the clustering process. Additionally, the choice of variables can greatly affect the results, as different variables might lead to different distance measures and consequently different cluster formations. Finally, the algorithm does not always yield the same clustering outcome; factors such as the method used for calculating distances (e.g., single-linkage, complete-linkage) and the initial conditions can lead to different results upon various executions, especially in the case of agglomerative clustering.