We present in this paper a Bootstrap Method to estimate a best value and its standard deviation for a discrepant set of data. The method is applied to the determination of the half-lives of 137 Cs, 90Sr, 252Cf, Tritium, 35 S, 55Fe, and 99Mo. The self-consistency of the method and its capability to reject outliers was tested with good results. The application of the method to the determination of covariance matrices was tried, with poor results.