Inraan, 1952; Folk and Ward, 1957, McCammon, 1962.) These formulas are 

 averages of 2, 3, 5, or more symmetrically selected percentiles of the 

 phi frequency distribution, such as the formula of Folk and Ward. 



M0 = ^ (4-3) 



where i|) is the particle size in phi units from the distribution curve 

 at the percentiles equivalent to the subscripts 16, 50 and 84 (Fig. 4-8); 

 4>^ is the size in phi units that is exceeded by x percent (by dry weight) 

 of the total sample. These definitions of percentile (after Griffiths, 1967, 

 p. 105) are known as graphic measures. A more complex method - the method 

 of moments - can yield more precise results when properly used. 



To a good approximation, the median, Mj is interchangeable with the 

 mean, (M) , for most beach sediment. Since the median is easier to deter- 

 mine it is widely used in engineering studies. For example, in one CERC 

 study of 465 sand samples from three New Jersey beaches, the mean computed 

 by the method of moments averaged only 0.01 millimeter smaller than the 

 median for sands whose average median was 0.30 millimeter (1.74 phi). 

 (Ramsey and Galvin, 1971.) 



The median and the mean describe the approximate center of the sedi- 

 ment size distribution. In the past, most coastal engineering projects 

 have used only this size information. However, for more detailed design 

 calculations of fill quantities required for beach restoration projects 

 (Sections 5.3 and 6.3), it is necessary to know more about the size dis- 

 tribution. 



Since the actual size distributions are such that the log of the size 

 is approximately normally distributed, the approximate distribution can be 

 described (in phi units) by the two parameters that describe a normal dis- 

 tribution - the mean and the standard deviation. In addition to these 

 two parameters (mean and standard deviation), skewness and kurtosis 

 describe how far the actual size distribution of the sample departs from 

 this theoretical lognormal distribution. 



Standard deviation is a measure of the degree to which the sample 

 spreads out around the mean and may be approximated using Inman's (1952) 

 definition, by 



'4> 



'84 ^16 



oa. = : , (4-4) 



where i^iqi^ is the sediment size, in phi units, that is finer than 84 per- 

 cent by weight, of the sample. If the sediment size in the sample actually 

 has a lognormal distribution, then a± is the standard deviation of the 



4-16 



