Eleanor Pairman and Karl Pearson 
253 
and asfain 
(xxxii) 
1-G51,2396h;+ 1-177, 1875h; 
•111,8()34«/, 
•915,5792».;- 2-384,2525h/ 
•298,1424h;, 
2-126,0271/i;/ 
a/ = _ •067,9063«/ - 
- •554,8634?i; + 
•332,2458h/ + 
+ 1-368,52437;;- 
a,; = - -988,7796/;,' + 2-823,7204/1,' ■ 
+ •472,0491<- -027,9508h/, 
2-497,6496/;/- 9-939,8504ho' + 13-394,6734/!/ 
- 7-822,9490/;,/+ 1-677,0510/// , 
= _ 7-413,4958/i/ + 25-320,8792/// - 3:1-899,3138/// 
+ 20-768,5399/// - 4-856,4601fl/. 
Hei'e as before //,/ = VgjN. 
We have accordingly to add the vahies given by (xxxi) to the expressions for 
the moments for the remainder of the frequency corrected for the abruptness by 
means of the series (xxxii). We propose to iHustrate our results on one or two 
numerical examples. 
(12) Illustration V. The following data provide the years of survival for 
10,000 persons, male and female, boi-n in England and Wales with congenital 
malformations*. 
Age at death Male Female 
Years 0—1 8762 8753 
1— 2 393 339 
2— 3 140 150 
3— 4 95 80 
4— 5 86 69 
5—10 
10—15 
15—20 
20—25 
25—30 
30—35 
35—40 
40—45 
45—50 
50—55 
55—60 
60—65 
65—70 
70—75 
185 
90 
86 
63 
45 
9 
18 
9 
9 
5 
184 
132 
86 
52 
40 
40 
17 
6 
23 
11 
6 
6 
6 
Totals 10,000 
10,000 
Now consider how we should endeavour to find the mean and standard di viation 
of such series under the old method. We clearly cannot use Sheppard's corrections. 
If we concentrate the deaths in the first year of life at 0-5, we shall certaiidy get 
too high a mean. Now Pearl has shown by taking Prussian statistics (Bionietrika, 
* Registrar-Geueral's Aniiunl Kfpui-I, p. '207, 1913. 
