Clustering technique in data mining has received a significant amount of attention from machine learning community in the last few years and become one of the fundamental research areas. Among the vast range of clustering algorithms, K-means is one of the most popular clustering algorithms. The basic principle of the K-means algorithm is to know how different distance measure is defined. It is a critical issue for K-means users. For example, how can we select a unique distance measure method for an optimum clustering task? Our research provides a statistical based Unique Distance Measure Approach for K-means(UDMA-Km) to this issue. We consider 112 supervised datasets and measure the statistical data characteristics using central tendency measure. Those data characteristics are split using well known entropy method to generate the rules. Finally, the generated rules are used to select the unique distance measure for K-means algorithm. The experiment is conducted within 112 problems and 10 fold cross validation methods. The most significant contribution of our study is that a new algorithm was created and the new algorithm can be used and has been used to solve any clustering tasks very quickly and provide much better optimum performance.