What is a true statement about input variables for k-means clustering?

The statement about input variables for k-means clustering being of interval measurement level is accurate. K-means clustering relies on calculating the means of the clusters to assess the distances between data points and their assigned cluster centroids. For this calculation to be meaningful, the input variables must be measured on an interval or ratio scale, where the distances between values are consistent and interpretable.

Interval measurement allows for the computation of various mathematical operations that are fundamental to k-means, including the calculation of mean values, variance, and the Euclidean distance between points. This ensures that the algorithm can effectively group similar data points together based on their numerical distance from one another.

While k-means can be applied to certain types of data, nominal measurements—like categories or labels—lack the necessary numerical properties to support the required calculations. Similarly, while it is beneficial for input variables to have some level of symmetry in their distributions, k-means can still function with non-symmetrical distributions as long as they meet the interval or ratio scale requirement. Thus, the most accurate assertion is that input variables should be of interval measurement level to ensure the clustering algorithm operates effectively.