With the advancement in survey and information technologies, comprehensive data collection has heightened concerns about personal privacy. Local Differential Privacy (LDP) provides an effective measure for privacy protection and has been successfully applied in both academia and industry. This paper focuses solely on the perturbation mechanisms under LDP, which typically include encoding, perturbation, and aggregation steps. Traditional LDP-based perturbation mechanisms are designed and analyzed under a sampling with replacement scheme. Our study explores perturbation mechanisms under a more refined sampling without replacement scheme, leading to more accurate variance analysis and efficient LDP mechanisms for whole population analysis. Among various mechanisms, the Improved Simmons(𝜋𝐵=0.50) achieves the lowest variance when the privacy budget is below a certain threshold, while ImprovedWarner excels when the budget is above this threshold. These assumptions generally hold true in real-world scenarios. In experiments using real-world datasets, the Improved Warner mechanisms significantly reduce the variance to 28.7% of its classic counterparts and the Improved Simmons(𝜋𝐵=0.50) mechanisms significantly reduce the variance to 11.7% of its classic counterparts. We also propose a practical deployment example of these improved mechanisms in real-world settings.