Vol. 6, 1920 STATISTICS: R. PEARL 431 
TABLE 2 
Pe;rcbntage Age Distribution of the Population of Certain Cities in 1910 
DAYTON 
INDIAN- 
APOLIS 
PROVI- 
DENCE 
CAM- 
BRIDGE 
NASH- 
VILLE 
BUFFALO 
NEW- 
YORK 
CLEVE- 
LAND 
AGE 
CLASSES 
(years) 
-24.10 
-24.23 
-30.05 
-30.26 
(N 
00 
T 
-48.61 
-74.42 
-74.51 
II 
■©■ 
II 
■e- 
■Q- 
II 
-0- 
II 
0- 4 
9.1% 
8.0% 
9.7% 
10.3% 
9.2% 
10.0% 
10.6% 
11.1% 
5-14 
15.4 
15.3 
16.5 
17.5 
17.8 
18.3 
18.1 
17.4 
15-24 
19.5 
19.4 
19.0 
18.4 
21.9 
20.6 
20.8 
20.5 
25-44 
34.6 
35.9 
34.2 
33.3 
32.2 
32.3 
33.9 
34.4 
45-64 
17.0 
17.0 
16.2 
16.0 
15.1 
15.5 
13.7 
13.4 
65 & over 
4.4 
4.3 
4.2 
4.4 
3.8 
3.4 
2.8 
3.0 
Totals 
100.0 
99.9 
99.8 
99.9 
100.0 
100.1 
99.9 
99.8 
to populations having relatively few persons in those groups. Further- 
more, it is evident that in each of the four pairs of cities compared the agree- 
ment between the two cities having nearly identical values of 0 is very 
close in respect of actual percentage distribution of the population. Day- 
ton and Indianapolis were for all practical statistical purposes identical 
in the age distribution of their populations in 1910. So were Providence 
and Cambridge, Nashville and Buffalo, and New York and Cleveland. 
In each case the curve for one distribution of the pair winds in and out 
about the path set by the other. Of course, we should get finer differen- 
tiations brought out by the </> function if we used 15 or 20 age classes in- 
stead of the 6 here employed. But for the purposes of the investigation 
in which I am using these functions, and for purposes of illustration of 
method 6 classes are sufficient. A word of caution must, however, be 
emphasized here. The reliability of 0 as an approximate index of differ- 
ences in age distributions of population is greater as we pass in either 
direction towards the ends of its range of values. In the case of popula- 
tions giving values of </> near the mean (say in the thirties for American 
cities) it may be necessary in order to get really differentiant values to 
calculate from a rather fine age grouping. 
In general it is believed that the function of an age distribution of a 
population here proposed will give, in a single numerical expression, a 
substantially accurate indication of the essential nature of that age dis- 
tribution, and will facilitate the differentiation and classification of popula- 
tions in respect of this characteristic for statistical studies, particularly 
by the method of multiple correlation. 
1 Papers from the Department of Biometry and Vital Statistics, School of Hygiene 
and Public Health, Johns Hopkins University, No. 16. 
2 Pearl, R., "Influenza Studies. I — On Certain General Statistical Aspects of the 
1918 Epidemic in American Cities," Public Health Repts., 34, 1919 (1743-1783). 
3 Glover, J. W., United States Life Tables, 1910, Bureau of the Census, 1916. 
