The issue was with the script, where update_cellsize_ranges was set to NO_CELL_SIZES. Due to this, MinPS, and MaxPS of the mosaic dataset items were not calculated (empty in the table). Change the add raster to mosaic dataset parameter to calculate the cell size range, and statistics are calculated without any issue.
arcpy.AddRastersToMosaicDataset_management(MDPath, "Raster Dataset", Filepath, "UPDATE_CELL_SIZES",.......