Quantization of 3D meshes involves representing the vertices of the mesh using a reduced number of bits, typically 10, 12, or 14 bits. This technique is particularly relevant for densely distributed 3D models, such as those representing human organs, which often require higher-precision floats with 32 or 64 bits. The increasing prevalence of IoT devices with limited computing resources has sparked interest in studying the conversion of dense 3D meshes into low-precision formats. However, surface smoothing is a significant challenge in medically acquired 3D meshes to eliminate the undesirable noise. It is observed that 10-bit quantization severely impacts the performance of state-of-the-art smoothing algorithms including Scale dependent umbrella (SDU), Mean curvature flow (MCF), Bi-normal filtering (BiNF), Bilateral filtering (BNF), L0 optimization, and Deep normal filtering network (DNF-Net). Some of these methods even do not complete their first round of iteration. A novel approach has been developed to address the surface smoothing challenges in 3D meshes with truncated vertex coordinates. The approach combines a central probability measure with Bayesian Averaging (BAM) and offers two versions for different scenarios. The first version, suitable for medical organs, utilizes a non-iterative process and reference models to achieve effective surface smoothing. By leveraging the central probability measure and BAM, it enhances the quality of medical organ meshes. The second version, more versatile for general-purpose meshes without reference models, employs an iterative process. It outperforms the existing methods by leveraging the central probability measure and BAM, particularly for meshes with dense point distributions.