The purpose of this study is to suggest a new modification of the usual ranked set sampling (RSS) method, namely; neoteric ranked set sampling (NRSS) for estimating the population mean and variance. The performances of the empirical mean and variance estimators based on NRSS are compared with their counterparts in ranked set sampling and simple random sampling (SRS) via Monte Carlo simulation. Simulation results indicate that the NRSS estimators perform much better than their counterparts using RSS and SRS designs when the ranking is perfect. When the ranking is imperfect, the NRSS estimators are still superior to their counterparts in ranked set sampling and simple random sampling methods. These findings show that the NRSS provides a uniform improvement over RSS without any additional costs. Finally, an illustrative example of a real data is provided to show the application of the new method in practice.