In this research investigation Analysis Of The Applicability Criterion For K Means Clustering Algorithm Run Ten Number Of Times On The First 25 Numbers Of The Fibonacci Series is performed. For this analysis RCB Model Of Applicability Criterion For K Means Clustering Algorithm is used. K-means is one of the simplest unsupervised learning algorithms that solve the well-known clustering problem. K- Means clustering algorithm is a scheme for clustering continuous and numeric data. As K-Means algorithm consists of scheme of random initialization of centroids, every time it is run, it gives different or slightly different results because it may reach some local optima. Quantification of such aforementioned variation is of some importance as this sheds light on the nature of the Discrete K-Means Objective function with regards its maxima and minima. The K-Means Clustering algorithm aims at minimizing the aforementioned Objective function. The RCB Model Of Applicability Criterion for K-Means Clustering aims at telling us if we can use the K-Means Clustering Algorithm on a given set of data within acceptable variation limits of the results of the K-Means Clustering Algorithm when it is run several times.