Statistical error caused by sample size (i.e. number of sample particles) has been studied by use of a computer simulation. Simulated results were compared with the theoretical equation in which a log-normal size distribution was assumed. The theory gave general analytical solutions for the distribution of sample mean diameter and the number of particles required to achieve a measurement within a certain error under a given confidence level. The computer simulation confirmed the theory. Therefore, the error caused by an inadequate number of sample particles or number of particles required in a measurement can be analytically estimated. It was also found that the number of particles required is reduced by both the evaluation basis and the assigned admissible error. However, fairly large numbers of particles are required for precise measurement.