Taking the antilogarithms, we have 



The period corresponding to P = 0.975 = antilog (1.0663) = 11.7 sec 

 The period corresponding to P = 0.500 = antilog (0.8450) = 6.99 sec 

 The period corresponding to P = 0.025 = antilog (0.6237) = 4.21 sec 



Any two of these three sets of values (P, x) determine the straight line (log-normal 

 distribution) plotted in Figure 28. 



The values of the mean and variance listed in Table 5 are in terms of natural logarithms. 

 Using the conversion log e x = 2.3026 log . x, we have 



Standard Deviation (log e x) = 2.3026 (0.1129) = 0.260 

 Variance (log e x) = (0.260) 2 = 0.0676 



Mean Value (log x) = 2.3026(0.8450) = 1.946 



TABLE 6 



Long-Term Distribution of Estimated Wave Periods at Station M 



Mean value and standard deviation were calculated from data given in Table 2. The data 

 are truncated at a wave period of 5 sec. 



Wave 



Period 



sec 



X 



Log x at 

 End of 

 Class 

 Interval 



Log 1Q x at 



Center of 



Class 



Interval 



A 



(Log 10 a;)-A r 



Measured 



from Point 



of Truncation 



a> = h - hy 



0? = 



(h-h T ) 2 



N 



Number of 

 Observations 

 Falling within 



the Class 



Percent of 



Variations 



Falling within 



Class Interval 



No 2 



Nco 



Cumulative 

 Percent 







5 



7 



9 



11 



13 



15 



17 



19 



21 



>21 



0.6990* 



0.8451 



0.9542 



1.0414 



1.1139 



1.1761 



1.2304 



1.2788 



1.3222 



1.3222 



0.7721 

 0.8997 



0.0731 

 0.2007 



0.0053 

 0.0403 



5,477 

 4,374 



9.80 



39.96 

 31.92 



29.028 

 176.272 



400.369 

 877.862 



9.80 

 49.76 

 81.68 



0.9978 



0.2988 



0.0893 



2,051 



14.97 



183.154 



612.839 



96.65 



1.0777 



0.3787 



0.1434 



382 



2.79 



54.779 



144.663 



99.44 



1.1450 



0.4460 



0.1989 



69 



0.503 



13.724 



30.774 



99.943 



1.2033 



0.5043 



0.2543 



3 



0.022 



0.763 



1.513 



99.965 



1.2546 



0.5556 



0.3087 



1 



0.007 



0.309 



0.556 



99.972 



1.3005 

 1.3222 



0.6015 

 0.6232 



0.3618 

 0.3884 



4 

 1 



0.029 

 0.007 



1.447 

 0.388 



2.406 

 0.623 



100.001 

 100.008 













12,362 





459.864 



2071.605 





*Tr 



is value is the point of 



runcation h T . 















Not 



e: This data is the basi 



s for Figure 28. 















50 



