Observed statistics of ocean waves have the statistical variability inherent to irregular waves. The variability is numerically examined by the linear simulation of the profiles of waves described with a directiona wave spectrum due to Mitsuyasu et al. Simulated wave profiles are sampled at the rate of ten data per significant wave period, and the length of a record is varied at 125, 250, 500, and 1000 data points.
　Standard deviations of wave statistics are mostly proportional to the inverse of the square root of the number of waves. The standard deviation of significant wave height and period for a record of one hundred waves are about 6 and 4 per cent of their values, respectively. Other representative wave heights and periods show greater variability than the significant ones. The variability of the root-mean-square value of wave profiles is slightly less than the significant wave height.
　Statistical analysis of a few data of observed wave records suggests the variability of real waves being greater than the prediction by the simulation data.