254 
On Corrections for Moment -Coefficients 
Vol. IV, p. 515) that as dechiced from data registered at short intervals of days, the 
mean of the total population of infants dying in the first year of life should be con- 
centrated at 0'3 instead of 0'5 year of life. But our infants with congenital mal- 
formations undoubtedly die earlier than the great bulk of normal infants. We 
might therefore hazard a concentration at 0'2; but this would be mere guesswork*, 
and what is more would not provide the proper corrections for concentrating in the 
case of other years of life. We obtain, however, by this process the following 
results : 
First Year concentrated at : 
Male 
Female 
0-2 
0-3 
0-2 
0-3 
Mean 
Standard Deviation 
] -2436 
4-5932 
1-3313 
4-5734 
1-5077 
5-7750 
1-5952 
5-7532 
The differences between the 0-2 and the 0-3 results are considerable and it will 
be found from the sequel that the 0-2 results are closest to the corrected results 
for both mean and standard deviation in the case of the male and the female. 
Indeed a quite i-easonable result might have been reached by centring the deaths 
in the first year of lifc at 0-2. But such a priori guesses must be at best risky. 
When we proceed to apply our method by cutting oft' the first year of life, we note 
at once that in this case, as in many other of a like J-distribution character, 
a grave difficulty arises, namely we have starting from the group 1 — 2 not got the 
groupings in year or five year ranges, for we have cut off" the first of our five year 
groups. We cannot therefore straight away apply our formulae based on the 
Euler-Maclaurin theory for equal subranges. The suggestion that at once occurs 
is to take year groupings fur our material. This of course would make no change 
in the first raw moment which would be the same whether we grouped into 
year or five year subranges on the supposition that we simply split up our 
frequencies into five equal groups for the five year periods. But there will be 
a change for the second and higher moments. For the second moment the total 
frequency of the five year group {nx) centred at x has to be multiplied by x~ + 2/i-^, 
where A = i of the subi-ange = one year, and similar corrections can be easily 
obtained for the higher moments. Of course this distribution of each five year 
frequency into five equal one year frequency groups is not satisfactory, but- with 
the irregular data as given it is, perhaps, as good a result as we can hope to get, 
until official statisticians rec<:>gnise the difficulty and table their statistics in a manner 
to meet it, i.e. in this case, it would mean either proceeding by four year groups 
after the 4 — 5, or giving the 5 — 6 frequency and then proceeding by five year 
groups 6 — 11, 11 — 16, etc. 
* Actually our auxiliary curve gives 0-210 for males and 0-20.5 for females for means of deaths in the 
first year of life. 
