A robust-symmetric mean: A new way of mean calculation for environmental data

Abstract

Environmental data seldom follow normal distributions, so how to calculate their means is a very important problem. Commonly used methods for mean calculation, such as arithmetic mean, geometric mean, and median, were evaluated. Arithmetic means should only be used when datasets follow normal distributions. Geometric means are suitable for datasets which follow log-normal distributions. Medians are a kind of robust treatment. However, their ‘efficiency’ is very low. Based on the methods described, two new ideas are developed: ‘robust’ and ‘symmetric’, for calculating means. As far as the symmetric feature is concerned, Box-Cox power transformation is better than logarithmic transformation. Robust statistics and Box-Cox transformation are combined to produce the ‘robust-symmetric mean’. As environmental data often follow log-normal or skewed distributions, this method is better than the previous ones and also is appropriate.