Editorial 
277 
In the special case of a normal distribution this reduces to 
} 7 1 
Mean a — o 
1 
m 32 M- 
This agrees with the value given in liitniietrlku, Vol. x, p. 526, Equation (xv), 
which is now generalised in (R) for a sample from material following any fre- 
quency distribution given by ^84, ySo and ^y. 
We must now adapt the result (R) for the array iip of a sample of size N. We 
need only to replace -^i and by S and H ,^ of our p. 278 and retain unto 
terms in We find 
Mean avp = a-tip 
1 
1 182 + 3 
8 
tip \ 
^) + ~ (m - 15/3,-^ - 2/3, - 4,S/3, - 103) 
This becomes in the case of normal fre(]uency 
3 31 
CTli,, — a n,, 
1 
4h^ 32n/ 
.(T''«). 
We can now find from (P). Subtracting the mean value [ha\ — aXg from ha 
., , 11 
we have, itX„ = K- ^ + , 
So" — \S<t] = a ]\a' + 
, 1 S/x, 
2 /Z, 
2M ^ m-' 
+ 
1 
_ 1_ f^f^Y 
128 ^ fi, J 
16 Va^. 
Hence squaring and taking means we find 
+ 
.(IT). 
64 I Va^T 
+ 
;8,-l_ 
I'M S2M' 
(4A - 7/3^ + 10 fi, - 24/3i - 23) 
1 
2VM 
1 - 
1 4^4 - 7^82' + lOyS., - 24^1 - 23 
16if /Sa - 1 
For a normal distribution this becomes* 
'^^ = - 81/) = ^JjWTT) """'^ 
* The value is in agreement with that given in Biomctriica, Vol. x, p. 526, Equation (xvi). 
■(V); 
.(W). 
..(X). 
