14. Using definitions given by Tukey (1977), the high and low hinges 

 define the 25 and 75 percent cutoffs, respectively. Together they provide a 

 good measure of the distribution of the changes by defining the range of the 

 mid-50 percent of the data. Their difference, or "hinge range," is a 

 convenient measure of variability. To further include a measure of the 

 distribution in a single parameter, Tukey also defines the "tri-mean" as: 



„ . low hinge + 2(median) + high hinge 



Tri-mean = ° ^^ ■ — = =- 



4 



Note that although these measures focus on the central 50 percent of the 

 data, they do not ignore the importance of the extreme values. In fact, 

 values that are outside the hinges (outliers) are clearly identified and 

 usually require individual attention. Example shoreline, slope, and volume 

 change tables, which include these summary statistics for the data in 

 Figure 2, are shown in Tables 2 and 3. 



15. The usefulness of these statistics is illustrated in Figure 3, 

 which is a "box and whisker" plot that graphically illustrates the 

 distribution of values given for each column in Table 3. It is quite clear 



Table 2 

 Example of Shoreline and Slope Tables 



Shoreline and Slope Changes at Atlantic City, N.J. 



Shoreline Foreshore Slope" 



Profile 



Survey 



Dates 



Change 

 (ni)I 



0.74 



First 



Second 





Line 



From 



18 



To 

 Dec 70 



Survey' 

 -0.038 



Survey^ 

 -0.024 



Change^ 



1 9 



Dec 70 



0.014 



2 9 



Dec 70 



18 



Dec 70 



-1.12 



-0.050 



-0.036 



0.014 



3 9 



Dec 70 



18 



Dec 70 



-7.50 



-0.026 



-0.020 



0.006 



4 9 



Dec 70 



18 



Dec 70 



6.49 



-0.046 



-0.030 



0.016 



5 9 



Dec 70 



18 



Dec 70 X 



5.86 



-0.040 



-0.026 



0.014 



6 9 



Dec 70 



18 



Dec 70 X 



3.70 



-0.020 



-0.028 



-0.008 



7 9 



Dec 70 



18 



Dec 70 



19.40 



-0.140 



-0.044 



0.096 



Median 









3.70 



-0.040 



-0.028 



0.014 



Tri-Mean 









3.35 



-0.040 



-0.029 



0.024 



High Hinge 









6.18 



-0.032 



-0.025 



0.056 



Low Hinge 









-0.19 



-0.048 



-0.033 



0.010 



Mean 









3.94 



-0.051 



-0.030 



0.033 



Standard Deviation 







8.33 



0.040 



0.008 



0.044 



Note: X = Extrapolated shoreline Intercept 



1 - Negative value indicates shoreline retreat. 



2 - Negative value indicates seaward sloping. 



3 - Negative value indicates steeper slope. 



11 



