Molecules undergo non-Brownian diffusion in the plasma membrane, but the mechanism behind this anomalous diffusion is controversial. To characterize the anomalous diffusion in the complex system of the plasma membrane and to understand its underlying mechanism, single-molecule/particle methods that allow researchers to avoid ensemble averaging have turned out to be highly effective. However, the intrinsic problems of time-averaging (resolution) and the frequency of the observations have not been explored. These would not matter for the observations of simple Brownian particles, but they do strongly affect the observation of molecules undergoing anomalous diffusion. We examined these effects on the apparent motion of molecules undergoing simple, totally confined, or hop diffusion, using Monte Carlo simulations of particles undergoing short-term confined diffusion within a compartment and long-term hop diffusion between these compartments, explicitly including the effects of time-averaging during a single frame of the camera (exposure time) and the frequency of observations (frame rate). The intricate relationships of these time-related experimental parameters with the intrinsic diffusion parameters have been clarified, which indicated that by systematically varying the frame time and rate, the anomalous diffusion can be clearly detected and characterized. Based on these results, single-particle tracking of transferrin receptor in the plasma membrane of live PtK2 cells were carried out, varying the frame time between 0.025 and 33 ms (0.03-40 kHz), which revealed the hop diffusion of the receptor between 47-nm (average) compartments with an average residency time of 1.7 ms, with the aid of single fluorescent-molecule video imaging.