Two available strength data sets of single-walled and multi-walled carbon nanotubes are analysed, and the effects of sample sizes on their tensile strengths are investigated. A minimum information criterion is applied to determine the optimal strength distribution. The results show that, in contrast to a two-parameter Weibull distribution, lognormal distribution seems to be a more suitable choice. A simple extrapolation of classical Weibull statistics to nanoscales may result in overestimation on the tensile strength of carbon nanotubes.