27C) 
Pecmvlmus ! 
from the mean vahie fi., of /x.., in the samples. Then fx., will not be /xo but be equal 
or expanding 
J_ / 1 5 
2ilf V ^ 4M ^ 8lf- 64M^ 
+ 
1 S/a. 
— 5 \ 
2 Mo 
^16 V/iJ \ ^ 23IJ 128 V/i. 
Now we need first the mean value of and for this purpose require the mean 
powers of ^ . These will be about the mean value of /i„ in samplas, i.e. ('l — jiZo 
.(P). 
and are*, if we use curved brackets to represent means 
=0, 
1 
M 
1^ 1 
M 
1 - 
- 8/3, - 6;'?, + 2) - ^(3/9, - 21/9, - 18^, + 26) 
+ ^. (-m - 33,8, - 22A + 54) + . . . 
3 (,8, - 1 + - 4/3, - 15y8./ - 24;8, + 48^, + 96,8, - 30) 
- jj-, (4/9, - 40,8, - 54,8/ - + 336,8, + 528/9, - 306 ) + 
where as usual 
= Ji.,-+'2lJi-I^\ and ^o,.+i = ('i2r+:! x Ms/Ms'"^'' 
and have reference to the sampled population. 
Substituting in (P) we have 
Mean a = a + [Scrl =a{\ — \a) say 
1 - sTf ^'^•^ + + 1^ ]p ^^^^ ~ + ^^^^ ~ ^^^^ " 
..(«)• 
The value for 
well-known, the two later values have been recently given by Professor 
Tchouproff, Bionictrilai, Vol. xii, p. 194. 
