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In this paper, three sampling-estimating strategies involving linear, balanced and modified systematic sampling are considered for the estimation of a finite population total in the presence of parabolic trend. Using appropriate super-population models, their performances are evaluated. For super-population models with constant variance, Yates corrected estimator under linear systematic sampling is shown to perform well. Choices of variance functions under which modified and balanced systematic sampling perform well are also identified based on extensive numerical studies.finite population, systematic sampling, super-population models, average variances,