This paper pays a special attention to the issue that there is a significant scatter of the stress-strain responses of a nuclear engineering material, 1Cr18Ni9Ti stainless steel pipe-weld metal. Statistical investigation is made to the cyclic stress amplitudes of this material. Three considerations are given. They consist of the total fit, the consistency with fatigue physics and the safety in practice of the seven commonly used statistical distributions, namely Weibull (two- and three-parameter), normal, lognormal, extreme minimum value, extreme maximum value and exponential.