Scheduling is a decision-making process through which large numbers of tasks compete for various system resources. The availability of limited resources makes scheduling a challenge. Among resources, the processoris the most important resource for in-time completion of tasks therefore; developing an efficient processor scheduler is still a topic of interest. We have applied a statistical approach that combines concept of median quartiles, upper quartiles and randomness to adjust the time quantum for each process with the objective of optimizing the allocation of CPU time to a set of processes. We have considered average waiting time, average turnaround time, and the number of context switches as performance metrics and compared our algorithm (IRRQR) with nine other dynamic time quantum adjustment algorithms. The comparisons with these algorithms reveal the effectiveness of IRRQR in terms of minimizing number of contexts switches up to 25%, average waiting time up to 13.7%, and average turnaround time by 8.4%.