List accessing problem has been studied as a problem of significant theoretical and practical interest in the context of linear search. Various list accessing algorithms have been proposed in the literature and their performances have been analyzed theoretically and experimentally. Move-To-Front(MTF),Transpose (TRANS) and Frequency Count (FC) are the three primitive and widely used list accessing algorithms. Most of the other list accessing algorithms are the variants of these three algorithms. As mentioned in the literature as an open problem, direct bounds on the behavior and performance of these list accessing algorithms are needed to allow realistic comparisons. MTF has been proved to be the best performing online algorithm till date in the literature for real life inputs with locality of reference. Motivated by the above challenging research issue, in this paper, we have generated four types of input request sequences corresponding to real life inputs without locality of reference. Using these types of request sequences, we have made an analytical study for evaluating the performance of MTF list accessing algorithm to obtain some novel and interesting theoretical results.