The multistage balanced groups ranked set samples (MBGRSS) method is considered for estimating the population mean for samples of size m = 3k where k is a positive real integer. It is compared with the simple random sampling (SRS) and ranked set sampling (RSS) schemes. For the symmetric distributions considered in this study, the MBGRSS estimator is an unbiased estimator of the population mean and it is more efficient than SRS and RSS methods based on the same number of measured units. Its efficiency is increasing in s for fixed value of the sample size, where s is the number of stages. For non symmetric distributions considered in this paper, the MBGRSS estimator is biased. The method is applied in a study of bioleaching.