320 
MR. R. A. FISHER ON THE MATHEMATICAL 
To illustrate a coarse grouping, take the group interval equal to the standard deviation : 
then 
CT 
*2tt 
and the error is 
— — e _27r ' sin 6 
with sufficient accuracy. The standard error of the mean being —%=, we may calculate 
n 
the size of the sample for which the error due to the periodic terms becomes equal to 
one-tenth of the standard error, by putting 
- e~ 2n *. 
whence 
For the second moment 
and, if we put 
there results 
n — 
10\/ n 7T 
_2 
e in2 = 13,790 billion. 
100 
„ v S CT ~ 
2 > 6 \ ~ 2f- 
-‘O’ _ j 2 — 2 tt 2 
= 4cr e , 
lOv 7 n 
n = swo W* =175 billion. 
The error, while still very minute, is thus more important for the second than for 
the first moment. 
For the third moment 
4 
A / \, 6 (T 6 ‘ j 1 6 6 / o .2 /»\ I i 
A s — (—) : 1 + — rn (tt s ~~ 6) r e - , 
e I -So- oS (T J 
iiV* 
putting 
v 
15a- 3 
10 Vn 
= 127Ta- 3 C _2ir ', 
n = 
900tt 
=147 billion. 
While for the fourth moment 
B. = (-)” 1 2^11- (tV-6)/-, 
S or 
S a 
2e* 
so that, if we put, 
V 90O" Q Q 2 4 —27T* 
-— = OZ7T <T <3 , 
10\/ n 
n = 
3200 
• e 4,r " = T'34 billion. 
7T 
