230 
On Theories of Association 
Ages of Husbands in the Eight Groups of Table XIX. 
True Mean Age of Husband 42-8306. 
J. UUI1U liUill 
Group 
By Gaussian 
By Yulean 
Value 
Deviation 
Value 
Deviation 
2 
3 
5 
6 
7 
38-57 
41-14 
40-48 
40-20 
40- 13 
41- 91 
-4-26 
-1-69 
-2-35 
-2-63 
-2-70 
-0-92 
46-32 
46-32 
45-66 
45-66 
45-66 
31 -32 
+ 3-49 
+ 3-49 
+ 2-83 
+ 2-83 
+ 2-83 
-11-51 
Mean 
From whole 
Eange 
2-43 
57-50 
4-49 
+ 14-67 
In five cases out of six the Gaussian gives better results than the Yulean in 
the simple matter of finding means even for such a skew distribution as those of 
ages of Husband and Wife. 
Now let us turn to the Ivy Leaves (Table of Breadth) * : 
By Gaussian 
By Yulean 
Groups 
Value 
Deviation 
Value 
Deviation 
5-95— 7-95 
7- 95— 8-95 
8- 95— 9-95 
9- 95— 10-95 
10-95—12-95 
11- 83 
12- 93 
12-60 
12-57 
12-87 
-1-39 
-0-29 
-0-62 
-0-65 
-0-34 
14-18 
11-06 
11-06 
11-06 
11-18 
+ 0-96 
-2-15 
-2-15 
-2-15 
-2-04 
Mean 
From whole Range 
0-66 
19-95 
1-89 
+ 6-74 
It will be seen that with one exception the true mean breadth (13'2148 for this 
very skew distribution of ivy leaves) would be substantially better found by using 
the Gaussian than by Mr Yule's assumptions. 
Taking the barometric height at Southamptonf we have, noting that the actual 
mean height is 29'9814, the results given in the table on the following page. 
In every case the Gaussian, we see, gives markedly better results than Mr Yule's 
method. 
We think it safe to conclude that the Gaussian can be used to give quite a 
good approach to the means of variates classed in "broad categories"; it is far 
* Phil. Trans. Vol. 197 A, p. 352. Breadth instead of Length taken for that character appears still 
more skew. 
t Phil. Trans. Vol. 190 A, p. 428. 
