IX.—CORRELATION. 
re asymmetrical, the skewness being positive for the rows at 
the top of the table (the mode being lower than the mean), and 
negative for the rows at the foot, the more central rows being, 
nearly symmetrical. The maximum frequency lies towards th 
upper end of the table in the compartment under the row an 
olumn headed “30-”. The frequency falls off very rapidly, 
wards the lower ages, and slowly in the direction of old age. 
utside these two forms, it seems impossible to delimit empirically; 
ny simple types. Tables V. and VI. are given simply as illus- 
rations of two very divergent forms. Fig. 31 gives a graphical 
representation of the former by the method corresponding to the 
histogram of Chapter VI., the frequency in each compartment 
eing represented by a square piliar. The distribution o 
requency is very characteristic, and quite different from that 
of any of the Tables I., IIL, III, or IV. 
6. It is clear that such tables may be treated by any of the 
ethods discussed in Chapter V., which are applicable to al 
ontingency-tables, however formed. The distribution may be 
investigated in detail by such methods as those of § 4, or tested 
or isotropy (§ 11), or the coefficient of contingency can be 
calculated (§§ 5-8). In applying any of these methods, however, 
it is desirable to use a coarser classification than is suited to the 
methods to be presently discussed, and it is not necessary to 
retain the constancy of the class-interval. The classification 
should, on the contrary, be arranged simply with a view to avoidin 
many scattered units or very small frequencies. A few examples 
should be worked as exercises by the student (Question 3). 
7. But the coefficient of contingency merely tells us whether, 
nd if so, how closely, the two variables are related, and muc 
more information than this can be obtained from the correlation- 
ble, seeing that the measures of Chapters VII. and VIII. can be 
pplied to the arrays as well as to the total distributions. If the 
wo variables are independent, the distributions of all paralle 
rrays are similar (Chap. V. § 13); hence their averages an 
ispersions, e.g. means and standard deviations, must be the same, 
n general they are not the same, and the relation between the 
mean or standard deviation of the array and its type require 
investigation. Of the two constants, the mean is, in general, the 
more important, and our attention will for the present be con- 
fined to it. The majority of the questions of practical statistic 
relate solely to averages: the most important and fundamental 
question is whether, on an average, high values of the one variable 
show any tendency to be associated with high (or with low) 
values of the other. If possible, we also desire to know how great 
divergence of the one variable from its average value is associate