If the data are truly lognormal, a minimum variance unbiased estimate of the mean is obtained by multiplying the GM by a factor that is always greater than 1 (Aitchison and Brown, 1969, page 45, eq. 5.40). However, this estimator is biased if the data are not truly lognormal, which may often be the case. Other estimators of central tendency include weighted means, and means that take into account a correlation that may exist between data values (discussed by De Wijs, 1951, 1953). These papers by De Wijs are concerned with ore assay values rather than radionuclides. However, both kinds of variables tend to follow lognormal-type distributions, and the objective of estimating "average" values is common to both fields of application. The applicability of De Wijs' References methods to radionuclide inventory studies needs to be evaluated. symmetric for primarily on the study of various estimators of central tendency distributions include Andrews et aZ. (1972) and Huber (1972). (1975, pp. 419-420) briefly related aspects of the problem. We may ask: Gilbert et al. Which is the more meaningful average for estimating, say, the inventory of 239Pu in surface soil? The average concentration is clearly related to the estimates of inventory obtained at safety-shot sites by Gilbert et al., 1975 (see Appendix A), since Area x Average Pu Concentration = Estimated Inventory (m?) (nCi/m*) (nCi) was used to estimate the inventory in each stratum. Hence, if the GM were used rather than the AM (the latter was used by Gilbert et al., 1975), a smaller estimate of inventory would result. The magnitude of the difference in estimates depends on the degree of skewness in the data. An example where the estimate of inventory changes by a factor of two depending on whether the AM or GM is used is given in Figure 6. In this figure, we plot the 239,240 py concentrations (nCi/g dry) obtained from 47 surface (0-5 cm) soil samples collected at random locations within stratum 6 in the GZ area of Area 13 (Project 57) (see Figure 4). Notice that 46 of the 47 observations fall between 0 and 22 nCi/g, but one observation is between 304 and 305 nCi/g. The effect of this one extreme point on the median, GM, and AM is indicated in the figure. If the outlying datum is deleted from consideration (which is not recommended since the datum does not appear to be a gross error), the AM drops from 14 to about 7 nCi/g, whereas the GM and median decline only slightly. Hence, if Gilbert et al. (1975) had deleted this one observation, their estimate of *3%py inventory for stratum 6 soil would have been about 8 rather than 19 curies. This in turn would have reduced the total estimated inventory for all six strata from 44 to 36 curies.!! The apparent precision of the estimate would also have improved due to the elimination of this single datum. 1lThe estimated total inventory for 23°%Pu in Area 13 (Project 57) is roughly 24 Ci if the GM is used in place of the AM and the datum 305 nCi/g is not deleted. 254