ALI QUOT SIZE(g) MEDIAN(e”) I lp 100 2.5 + 1.66 1.78 1.92 6 0.5085 0.4823 0.5742 0.2217 0.6503 0.0890 I = 204 100 4 “ Zz LOGNORMAL DENSITY FUNCTION __) = 155 o = ira > 10+ = "05 5 0 6 —10q 2 0 15 (109, x _ i 2 f(x) = oer oo lg 1 Figure 5. J Ww. 2 1 3 4 5 6 241 Am CONCENTRATION (x) Density Functions of 1, l 7 1 8 10, and 100 g Aliquots Assuming the Observed Data (Figure 1) are Lognormally Distributed with Parameters u and o as Estimated from the Data. results* for aliquot sizes of 1, 10, and 100 g. The median and mean of a lognormal distribution are given by exp(u) and exp(y + 92/2), respectively. We see from Figure 5 that the estimates of u increase while those of o decrease as aliquot size increases. Hence, as fi increases from 0.5085 to 0.6503, the median necessarily increases from 1.66 to 1.92. However, the mean remains relatively constant at 1.87, 1.82, and 1.92 for 1-, 10-, and 100-g aliquots, respectively, due to the decrease in 6 for the larger aliquot sizes. Indeed, as o approaches zero the lognormal distribution approaches the symmetric normal distribution for which the mean and median are identical. The above remarks for the *%u and o are estimated as the mean and standard deviation of the log.- transformed data. 422