Estimation of population characteristics has been an area of interest for many years. Various estimators of the population mean and the population variance have been proposed from time-to-time with a view to improve efficiency of the estimates. In this paper, we have proposed some estimators for estimation of the general population parameters. The estimators have been proposed for single-phase and two-phase sampling using information of single and multiple auxiliary variables. The bias and mean square errors of the proposed estimators have been obtained. Some comparison of the proposed estimators has been done with some existing estimators of mean and variance. Some specific cases of the proposed estimators have been discussed. Simulation and numerical study have also been conducted to see the performance of the proposed estimators.