90 riKH'KKDINUS OF THK ANATOMICAL AXI) ANTHROPOLOGICAL 



ordinate, i.e., the mode would not coincide with the mean. The 

 curve obtained in this latter case has been called the Skeir Hi mutual. 



The curve of frequency obtained from measurements sometimes 

 takes the form of the skew binomial. This might happen, for ex- 

 amide, if there were two races among the group of people measured. 



The binomial curves are not convenient to work with on account 

 of the difficulty of calculating the coefficients when the number of 

 terms in the expansion is very large. We use, therefore, instead of 

 the binomial curves smooth curves which make a very good fit with 

 the binomial curves, and which can be represented by equations 

 which are much more convenient to work with than a long binomial 

 expansion. 



Normal Curre. The smooth curve, which corresponds to the 

 symmetrical binomial, is called the Normal Curve, and its equation 

 about the mean is 



z 2 

 9-9*- w 



In this equation y represents the maximum ordinate or fre- 

 quency, e is the base of the Napierian logarithms, and o- is the 

 standard deviation, a term which we shall discuss later on. 



If we can fit a normal curve to the curve of frequency obtained 

 from our observations, we can calculate by this equation the fre- 

 quency y at any distance x from the mean dimension. 



The normal curve can also be shown to represent the frequency 

 curve of deviations of other samples of the population from the 

 observed sample, and its properties are therefore utilised in cal- 

 culating what is called the probable errors of the various quantities 

 evaluated from anthropometric statistics. 



Standard J)eriation. In measuring a large number of individuals, 

 even when they all belong to one pure race, we always find that there 

 are a certain number of individuals whose dimensions are greater or 

 less than the mean dimensions. It is very desirable to find some 

 expression for the value of this deviation from the mean. What is 

 the best expression for the deviation of the whole group that has 



