What happens when standardizing variables in clustering?

When standardizing variables in clustering, it can indeed change the clustered groups significantly. Standardization typically involves rescaling the data so that each feature contributes equally to the distance calculations, often by transforming the data to have a mean of zero and a standard deviation of one. This process is crucial in clustering because many clustering algorithms, such as K-means, rely on distance measures (like Euclidean distance) that can be heavily influenced by the scale of the data.

If variables are on different scales—such as income (in thousands) and age (in years)—the variable with the larger scale can dominate the clustering results. By standardizing, you ensure that each feature impacts the clustering process equally, which can lead to different clusters than those identified without standardization. As a result, the identified groups may change significantly, reflecting the underlying structure of the data more accurately once scaled appropriately.

In contrast, the other options imply outcomes that do not reflect the impact of standardization accurately. For instance, stating that it always results in the same clusters overlooks the core principle of scaling affecting distance calculations. Similarly, saying it is irrelevant for clustering results ignores the fundamental role of distance in clustering algorithms. Finally, claiming it exclusively affects hierarchical clustering fails to recognize that standardization