1 



1 1 1 1 1 1 1 



1 1 



1 1 1 



1 1 1 1 1 



2 



1 1 



1 0.5 



1 1 



mm 



1 



0.1 

 1 1 



0.05 



1 1 



-4 



Figure 3. The normal curve (for y = 2.0, a = 0.70). Shaded 



area for interval ± la from mean (y) contains 



the central 68 percent of the area under the curve 

 (adapted from Krumbein, 1957) . 



following estimate of the mean which is statistically more efficient 

 and less biased than the median for cases where the actual gsd is not 

 completely symmetrical. 



M^ = 



)16 



(4) 



For a symmetrical distribution, equation (4) will produce the same value 

 as the median. Sx and M^x (eqs . 3 and 4) are probably the best esti- 

 mates of a and y (Inman, 1952) for describing unimodal sedimentary 

 grain-size distributions. 



A common way to obtain these parameters is by using a graphical 

 technique (Fig. 4) . The sample size data are plotted as a cumulative 

 distribution on log (phi) probability paper. This paper is constructed 

 so that a lognormal distribution will plot as a straight line. The plots 

 of sample distributions that are asymmetric will not be straight. The 

 degree of asymmetry, or nonnormality, can be determined by comparing 

 the observed distribution with a straight "approximation" curve drawn 



13 



