Miscellanea 
TABLE V. 
x-sum of Table IV., i.e. a table giving all cases fur x, y group 
and over in Table III. 
^11 
X 
Totals 
1 
2 
3 
5 
1 
200 
196 
17G 
97 
22 
691 
2 
159 
157 
143 
74 
19 
552 
y 
3 
112 
111 
102 
63 
17 
405 
4 
38 
37 
37 
26 
10 
148 
Totals 
509 
501 
458 
260 
68 
1796 
The totals in the right-liand column of Table IV. give the first sum of the total in the right- 
hand column of Table III. and are the same as the column x=\ in Table V. The total 
of Table III. or the smn of col. 1 in Table IV. gives the mean of the j/'s (509-=- 200) ; similarly 
the sum of the row y= 1 gives the mean of the x'a (691 -=-200). 
The total of Table V. gives the a^y-moment (1796) and the .r-standard deviation is found by 
forming from the first row the .series 691, 491, 295, 119, 22 and summing it, i.e. 1618. The 
second moment about the mean can then be found ; the numerical working being as follows : 
.t'-mean = 691 -^ 200 = 3-455, 
v<> = 2S^/Sj — d{l+d) by formula given above 
1618x2 
200 
3-455 X 4-455 
= -7t 
Similarly with the j/-moments 
!/-mean = 509 ^ 200 = 2-545, 
_ (509 + 309 -t- 150 -f- 38) X 2 
200 
2-545x3-545 
= 1-038. 
1796 
The .f?/-moment = - 2-545 x 3-455 
200 
= •1870, 
r = -1870 V-788X 1-038 
= •207. 
In this example the moments have not been adjusted as the totals of the rows did not seem to 
warrant the assumption of high contact. 
Table V. can be formed directly from Table III. but it is a little troublesome to do so 
at first. The method can best be understood by seeing how any item is made up ; thus 
63 = 30 + 174-26-10, 97 = 20 + 74-t-22- 19, 102 = 28-1-63 + 37-26 and so on. 
It is not difficult to see how Table V. succeeds in giving the A'j/-moment ; we have merely to 
remember the numbers by which the various terms in a correlation table have to be multiplied 
to produce the required result. The final item in Table III. for instance has to be multiplied 
by 20. It occurs in every item in the .v = 5 column of Table IV. and therefore in every item of 
Table V. ; there are 20 items. Similarly the entry 28 in Table III. has to be multiplied by 9 ; 
Biometrika iv 48 
