The measurement errors exist and sample survey results are always uncertain because only a portion of the population is measured. Larger samples and superior measurement tools can help to reduce this uncertainty. The statistician may work with a high number of strata in surveys where there are numerous effective stratification criteria. Even the extreme scenario of a few units like only one or two observations per stratum is used occasionally. In that case, the collapsed stratum technique is the standard method for estimating variance. This method, however, is biased and results in an overestimation of the variance. This paper developed a variance estimator for the total population under fine stratification using a bootstrap bias corrector technique to overcome the drawbacks of previously explored estimate approaches. The estimator’s properties have been also derived, and the simulation results show that the proposed estimator outperforms the current ones.