s 
s 
270 Oil 'Best' Values of Constants in Frequency Distributions 
and the equations (2 a) take the form 
1 
+ s 
\n,p (] 
S 
(l-p) 
1 1 
[m 
1 
^ ' I - 1 
1 
1 
(1 — p) 
(jH-s)(log,;; + | + y-^--^ 
+ 
1-S+] 
, 11 1 \2 1 1 
+ 1/ ■ ■ 
while the approximate formulae of the type (2 b) are 
n 
--{l-p) 
1 
(^-s+1) 
Ai! 
^5 //V - s 
n, p{l - p) 
+ 2S 
log^,p 
] 1 
n,p(l - p) 
1 1 
1 
Al 
+ ... + 
I- s+l 
M9). 
= 2;S U 
«,J9(l-29) 
- s) (log, + I + ~ f . . . + ) A^ 
+ 2;S 
I - s+l 
Illustration V. Weldori's Dice Data. 
For illustration are used the following data due to the late Professor W. F. R. 
Weldon*. They give the observed frequencies of dice with five or six points when 
a throw of twelve dice was made 26306 times. 
TABLE VIII. 
Number of dice 
in cast with 5 
or 0 points 
Observed 
frequency 
Binomial by 
method of 
moments 
Improved binomial 
(o) by a 
minimum 
Improved binomial 
(b) by a 
minimum 
0 
185 
189-679 
190-651 
190-659 
1 
1149 
1154-441 
1157-607 
1157-600 
2 
3265 
3223-426 
3226-085 
3225-959 
3 
5475 
5461-01 
5458-07 
5457-78 
4 
6114 
6253-64 
6245-98 
6245-71 
5 
5194 
5101-31 
5095-82 
5095-79 
6 
3067 
3041-04 
3041-47 
3041-69 
7 
1331 
1335-82 
1339-55 
1339-81 
8 
403 
429-627 
432-815 
432-984 
9 
105 
98-865 
100-351 
100-419 
10 
14 
15-5133 
15-9413 
15-9595 
11 
4 
1-57640 
1-65879 
1-66210 
Phil. Mag. July, 1900, p. 167. 
