MISCELLANEA. 
Notes on Statistical Processes. 
By W. PALIN ELDERTON, Actuanj. 
I. 
An Alternative Method of calculating the Rough Moments from the 
Actual Statistics. 
Let s be the position of any term in the series and f{s) the frequency corresponding, then the 
following table (page 375) explains itself 
Consider the line opposite the first term and we notice that the sum of the series is given by 
the first summation »S'i and that the second which we will call <S'2 gives the first moment of 
the whole distribution about a vertical through a point situated at unit distance before the 
point corresponding to /(I). Still considering only the first line we see that »S'3 gives each 
— |- 3. ^ 71"^ •\- "it 
function multiplied by — ^— — or — - — , i.e. (wi2' + Wi')^2 where 'rti' is written for the rough 
„. , „ . m3^3n2 + 2m , „ . w* + 6?i3 + 11m^ + 6» , , 
moment. Similarly »?4 gives ^ and gives ^ , and hence 
*>3 = 
2 
6 ' 
+ Qm^ + 1 Imi + 6?«i' 
24 
A numerical example is as follows. 
TABLE II. 
Function 
1st sum 
2ud sum 
3rd sum 
4tli sum 
239 
524 
978 
1648 
2587 
157 
285 
454 
670 
939 
93 
128 
169 
216 
269 
29 
35 
41 
47 
53 
6 
6 
6 
6 
6 
524 
978 
1648 
2587 
3854 
