VCH.. 8, 1922 
STATISTICS: J. R. MINER 
107 
The standard errors of sampling of births and deaths will be: 
^/ B{N-B) _ J D{N-D) 
Whence = — = \ — ^ = ^ = 
and the probable error of the birth-death ratio will be^ 
B l \ - B/N 1 - P/N 
B ~^ D 
(i) 
since r = 0, being the correlation of errors of sampling of births and deaths. 
As B and D are small as compared with N we may write this approximately : 
^^j 1^1= 67.449^ Vs + I^ (ii) 
This form has the advantage of not involving A^, so that if the numbers 
of births and deaths in a community are known but not the population, 
the probable error of the birth-death ratio may still be found. 
For Baltimore in 1917 
N = 594,637 
B = 15,040 
D = 11,355. 
Therefore by (i) 
i 15040 11355 
1 - 
PE, ,= 67.449 1^ J -^^^^^^ + _^94637 
^^10^^ 11355 \ 15040 ^ 11355 
CO / 0.9747 0.9809 , 
89.34-%/. 1 = 89.34 V. 00006481 -j- .00008638 
15040 11355 
= 89.34 X .01229 = 1.10 
By (ii) 
( inn R ) 67.449 ^-^2^ -\/ — 1 — = 89.34 V .00006649 + .00008807 
U_oo_B/ 11355 If 15040 11355 
1 ^ S 
= 89.34 X .01243 = 1.11. 
In using these formulae it should be borne in mind that the expression 
for the standard deviation of an index, which has been used in their der- 
ivation, is obtained on the assumption that deviations are small compared 
with the mean values of the variables. This will be true if B and D are of 
