108 



2. Normal curves. It has long been recognized that 

 if we measure a great number of individuals and if then 

 we plot the frequency with which the différent statures 

 occur, thèse frequencies arrange themselves in a regular 

 curve. The following example will illustrate the fact. It 

 summarizes the measures of the length of 8585 ') men 

 between the âges of 23 and 50 years in Great Britain. 



The meaning of this table is perhaps best seen by an 

 example. From the first part of the table we learn that 

 among a total 8585 men 169, that is the fraction 0.020 

 of the whole, hâve a height between 62 and 63 inches 

 and further that the fraction 0.037 of the whole is below 

 63 inches. The name "Scheme" has been given by Gai ton 

 to the curve which we get when we plot the numbers of 

 the 4''' col. as ordinates corresponding to the numbers 

 of the first col. as abscissae. The curve is represented 

 in fig. 1. 



In what follows we will, following the gênerai use, 

 designate the abscissae by the letter x, the ordinates by 

 the letter y. 



In the second part of the table the statures hâve been 

 expressed, not in inches, but in fractions of the average 

 stature, which in the présent case (see last line of table) 

 turns out to be 67.5 inches. 



In fîg, 1 is also shown the frequency curve wich we 

 get by plotting the frequencies of the 3^^ col. as y's over 

 the numbers of the first Col. as x's. 



It will be seen at once that whereas (to take an example) 

 the frequency of stature below 65 inches is represented 

 in the frequency curve by an area — the area of the 

 curve below the ordinate of jc = 65 — it is represented 

 in the scheme by this ordinate itself. Quite generally 

 frequencies are represented by areas in the frequency 



1) Taken from: Report of the Brit-Assoc. 1883, p. 256. 



