For k-means clustering, which statement is true about input variables?

The statement that input variables should be meaningful to analysis objectives is essential in k-means clustering. When selecting input variables, relevance to the analysis ensures that the resulting clusters provide insights that align with the goals of the study. Meaningful variables contribute to the identification of patterns and relationships within the data, which enhances the interpretability and usefulness of the clusters generated by the algorithm.

In k-means clustering, the algorithm attempts to partition the data into clusters based on the mean distances between data points. If the input variables are not meaningful, the clusters may not accurately reflect the underlying structures of the data or serve the intended analysis purpose. Therefore, ensuring that the input features are aligned with the analysis objectives is critical for successful clustering and for drawing valid conclusions from the results.

The other options do not support the effectiveness of k-means clustering. Including categorical data could complicate the distance calculation, as k-means typically works better with continuous data. Outliers can skew the centroids significantly, thereby distorting the clustering outcomes. Lastly, using variables that are unrelated to the analysis context can lead to irrelevant clustering results, obscuring the discovery of meaningful patterns.