K-means is a widely used partitional clustering method. While there are considerable research efforts to characterize the key features of K-means clustering, further investigation is needed to reveal whether and how the data distributions can have the impact on the performance of K-means clustering. Indeed, in this paper, we revisit the K-means clustering problem by answering three questions. First, how the "true" cluster sizes can make impact on the performance of K-means clustering? Second, is the entropy an algorithm-independent validation measure for K-means clustering? Finally, what is the distribution of the clustering results by Kmeans? To that end, we first illustrate that K-means tends to generate the clusters with the relatively uniform distribution on the cluster sizes. In addition, we show that the entropy measure, an external clustering validation measure, has the favorite on the clustering algorithms which tend to reduce high variation on the cluster sizes. Finally, our experimental results indicate that K-means tends to produce the clusters in which the variation of the cluster sizes, as measured by the Coefficient of Variation (CV), is in a specific range, approximately from 0.3 to 1.0.