as deeply into the beach. This difference is partly compensated for by 

 the fact that CERC sampled a few times a month which should have the same 

 effect as sampling a few layers at one time. 



Since McMaster lists quartile-size fraction of each sample, the sample 

 mean of his samples was probably calculated using: 



Mn^ = (<i'25 + '('SO + <)'75)/3 , (5) 



instead of the five percentile mean (Fig. 12) used to compute CERC's sam- 

 ple means. Equation (5) has a statistical efficiency of about 88 percent 

 (McCammon, 1962) while five percentile mean has an efficiency of 93 per- 

 cent, so the error due to the method of calculation is probably not sig- 

 nificant for these data. 



McMaster wet-sieved his samples to remove any size fraction less than 

 0.053 millimeter; the CERC samples were not wet-sieved. However, analysis 

 of CERC's data showed that only one dry sieve sample had a significant 

 frequency percent (0.5 percent) finer than 0.064 millimeter, but none of 

 the RSA samples gave zero percent for this size class. 



Another difference was that McMaster also sieved for gravel, but only 

 two of his samples taken from the same area considered in CERC's study 

 had a recordable gravel frequency percent. In these two cases, the gravel 

 content was 0.1 and 0.4 percent and these percentages could not signifi- 

 cantly affect the quartile measurements used to characterize the size of 

 his samples. A final minor difference is that McMaster used 0.5-phi sieve 

 intervals which included 0.25, 0.75, etc.; CERC used 0.5-phi intervals 

 which included 0.00, 0.50, etc. Both McMaster and CERC used the retaining 

 sieve definition of size. 



7. Sample Average and Profile Average . 



To determine trends in the data, it is useful to deal with averages. 

 Since each sample mean is identified by the three space coordinates and 

 the time of sample collection (Apps. A and B of Ramsey and Galvin, 1971), 

 there are a number of possible ways to average the data. In this report, 

 sample means are segregated by profile line, position on profile, or month, 

 and then averaged as "sample averages" or "profile averages". A sample 

 average is obtained by adding sample means and dividing by the number of 

 samples. A profile average is the average of a collection of sample aver- 

 ages, in the case where each sample average is from a different profile 

 line. In effect, sample averages are weighted by the number of samples in 

 the collection, and profile averages are weighted by the number of profiles 

 in the collection. 



To summarize the definitions used here, a sample mean is the mean of 

 the size distribution of a single sand sample. A sample average is an 

 average of selected sample means at one locality or one profile. A pvofile 



34 



