RA CITEPS 
VII. —AVERAGES. S147 * 
oo > 
differ : (1) they may differ markedly in position, z.e. ir the Palubso th ek 
of the variable round which they centre, as in fig. 2. 4, or (2) 
they may centre round the same value, but differ in t Hinge of 
variation or dispersion, as it is termed, as in fig. 20, B. ours io) # 
the distributions may, differ in both characters at once, as in ¥&20,'"'" 
C, but the two properties may be considered independently. 
Measures of the first character, position, are generally known as 
averages ; measures of the second are termed measures of disper- 
sion. In addition to these two principal and fundamental 
characters, we may also take a third of some interest but of much 
less importance, viz. the degree of asymmetry of the distribution. 
ee ee 
2 
ee 
L.. = 
12 
Fie. 20. 
The present chapter deals only with averages; measures of 
dispersion are considered in Chapter VIII. and measures of 
asymmetry are also briefly discussed at the end of that chapter. 
3. In whatever way an average is defined, it may be as well to 
note, it is merely a certain value of the variable, and is therefore 
necessarily of the same dimensions as the variable: z.e. if the 
variable be a length, its average is a length ; if the variable be a 
percentage, its average is a percentage, and so on. But there are 
several different ways of approximately defining the position of a 
frequency-distribution, that is, there are several different forms of 
average, and the question therefore arises, By what criteria are we 
to judge the relative merits of different forms? What are, in fact. 
the desirable properties for an average to possess? 
a 
B 
Cc