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.
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Bakr, A. A.; Gelhar, L. W.; Wutjahr, A. L.; MacMillan, J. R.: Stochastic analysis of spatial variability in subsurface flows 1: Comparison of one and three-dimensional flows. Water Resour. Res. 14, 263–271 (1978).
Box, G. E. P.; Cox, D. R.: An analysis of transformations. Journal of the Royal Statistical Society, Series B 26(2), 211–252 (1962).
Chapman, R. P.: Some consequences of applying lognormal theory to pseudolognormal distributions. Mathematical Geology 8(2), 209–214 (1976).
Dagan G.: Models of groundwater flow in statistically homogeneous porous formations. Water Resour. Res. 15, 47–63 (1979).
Dagan G.: Analysis of flow through heterogeneous random aquifers by the model of embedding matrix 1: Steady flow. Water Resour. Res. 17, 107–121 (1981).
Jensen J. L.: Use of geometric average for effective permeability estimation. Mathematic Geology 23(6), 833–840 (1991).
Jobson, J. D.: Applied Multivariate Data Analysis. Vol. I: Regressing and Experimental Design. Springer Verlag, New York 1991.
King, P. R.: Effective values in averaging. In: Edwards S.; King P. R. (eds.), Mathematics in Oil Production, pp. 217–234. Oxford University Press, Oxford 1988.
King, P. R.: The use of renormalization for calculation effective permeability. Transport in Porous Media 4, 37–58 (1989).
Krige, D. G.: A statistical approach to some basic mine valuation problem on the Witwatersrand. J. Chem. Metall. Mining Soc. S. Aft. 52, 119–139 (1951).
Krige, D. G.: On the departure of ore value distributions from lognormal models in South African gold mines. J. S. Afr. Inst. Mining Metall. 61, 231–244 (1960).
Miesch, A. T.: Methods of Computation for Estimating Geochemical Abundance. U.S. Geological Survey Open-file Report, 76-772 (1967). 1140 pp.
Miesch, A. T.: Geochemical survey of Missouri — Methods of sampling, laboratory analysis and statistical reduction of data. U.S. Geological Survey Professional Paper 954-A (1976). 39 pp.
Miesch, A. T.; Riley L. B.: Basic statistical methods used in geochemical investigations of Colorado Plateau uranium deposits. HIMMP Trans. (Mining) 220, 247–251 (1961).
Richardson J. G.: Letter to the Editor, J. Pet. Tech. 42, 1524 (1990).
Sanford, R. F.; Pierson, C. T.; Crovelli, R. A.: An objective replacement method for censored geochemical data. Mathematical Geology 25(1), 59–80 (1993).
Sichel, H. S.: New methods in the statistical evaluation of mine sampling data. London, Inst. Mining and Metall. Trans. 61, 261–288 (1952).
Sichel, H. S.: The estimation of means and associated confidence limits for small samples from lognormal populations. J. S. Aft. Inst. Mining and Metall., Symposium: Mathematical Statistics and Computer Application in Ore Valuation, 106–123 (1966).
Zhang, C. S.; Zhang, S.; Zhang, L. C.; Wang, L. J.: Background contents of heavy metals in sediments of the Yangtze River system and their calculation methods. Journal of Environmental Sciences 7(4), 422–429 (1995).
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Zhang, C., Zhang, S. A robust-symmetric mean: A new way of mean calculation for environmental data. GeoJournal 40, 209–212 (1996). https://doi.org/10.1007/BF00222547
- Normal Distribution
- Environmental Management
- Environmental Data
- Skewed Distribution
- Logarithmic Transformation