Estimating the standard deviation from extreme Gaussian values

We derive an estimator for the standard deviation of a Gaussian random variable that uses the maximum of two observations on the random variables. The process is repeated until the variance of the estimator or the degree of confidence reaches a predetermined level. The estimator is unbiased and consistent, and its variance is only marginally larger than the standard square root of the sum of the squares estimator. Moreover the computation of an estimate requires only a sequence of comparisons of two numbers followed by an addition.