Due to various problems inherent in the calculation of statistical wind direction parameters over different averaging times, e.g., mean direction and standard deviation for periods of 10-60 minutes, as well as situations where the raw direction samples are not available, a new minimum variance approach to estimating these parameters has been developed. This approach does not require raw direction samples, but instead uses one-minute means and standard deviations as inputs. It also has the desirable property that estimated mean directions are naturally "weighted" by the magnitude of the standard deviation associated with that direction, i.e., more tightly grouped sets of directions are given a correspondingly higher weight in the variance estimate. The new algorithm thus yields a minimum error estimate, which approaches the arithmetic mean in the limit. This algorithm has potential utility in data post-processing applications, as well as atmospheric and dispersion modeling applications using historical data.