20 



Uli tlic Syatematic Fi(ting of Curces 



be a inost iindesirable reprcsuntatiuu of thc facts, für it has twisted and curled to 

 account for error as well as to give the general sweep of the observations. 



(l-i) Illustnition VII. As a secnnd illustration of parabola-fitting I will take 

 froiu the Italian inarriage statistics of Perozzo thc modal ages of bridegrooms of 

 brides of giveii ages. With some simple interpolations I have determined these 

 from Perozzo's tables* as approximately the following: 



New let US take 43'5 as the origin of age for thc mau, and 30'ö as that for 

 the woman ; then if i/ be the iiian's age aud .v the wouiau's, we have thu following 

 series of poiuts : 



x= 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 

 y=ll-.3, lü-ö, 10, 9-.5, 9, 7-5, 6-5, 5, 4. 2, •_', 1, 0, 0, 0, 0, 

 a-= -1, -2,-3,-4,-5, -f), -7, -8, -9,-10,-11,-12,-13,-14,-15, 

 ?/= 13-5, 14-5, l.rö, IG, lü-."), Ki 7, I7ö, 17ö, 17-75, 18, 18, 18, 181. 18-3, lS-5. 



The ränge is thus 2^ = 30, and conuuntrating and then using the eorrective 

 forinulaj for trapezoidal polygons given in § 10 we easily find 



y„ = 10-78G7, 



\, = _ •348,5000, \, = 173,6922, 



X,= -299.9504, X^ = - -137,7881. 



X;, = - ■19.s,1573, X,. = -1 23,0257. 



The e's were then determined from the X's by the forraula; of § 12 aud we have 

 for the series of parabohus, if / = 15 yeai-s : 



* Reale Accademia äei Lineti. Aiiuo ccLXXix, 188'2. Nuove Applicazioni del Calcolo delle ProbabilitK. 



