KmsTiNE Smith 
269 
The numerical values of the constants of the series and of the 'goodness of 
fit' are 
TABLE VII. 
m, 
P 
dm 
Poisson ... 
Poisson improved 
•501000 
•509700 
6^865 
6^672 
•231 
•246 
~ 4b86 
- 1-21 
This table is of interest because it illustrates the apparent paradox, already seen 
in the case of the second Gaussian curve illustration, that the ' mean ' is not neces- 
sarily the 'best value' of the constant termed the 'mean.' 
(5) Fit of a Binomial to Binomial Data. 
Let be equal to the (s + l)th term of the binomial {p + qY, where 
p + q = \, or to 
^l{l- s+ 1). 
S\ 
we then find 
dn^ _ I — pi — s _ m — s 
dp ~ p{l-p) ~ ""'pil-p) ' 
where m is the mean or stand for I (\ — p). 
dp^ p^ (1 — p)' 
{{I -pi- sf -{I -pi- s) (1 - 2p) - Ip (1 - p)\ 
dn^ _ /, 1 
+ 
I - ] 
p^ {1 — 
+ 1 
{{m - s)2 + {m - s) (1 - 2p) + mp}, 
d^n, _ fA 11 
dl^ 
dldp p {I — p) 
Hence we have 
I ' l-l 
l-s 
- s + l)' 
7)1 — S 
(loge 
I ' l-l 
- S 
