118 On the Prohahle Errors of Frequency Constants 
Correlation of errors of grades as found by viean and standard deviations. 
(") 
Quartile and Quartile : 
•6294, 
(b) 
Median and Quartile : 
•9026, 
(c) 
Median and Decile : 
= 
•6152, 
(d) 
Decile and Decile : 
•0982, 
(e) 
Quartile and Decile : 
= 
•9579, 
(/) Quartile and Decile : 
•3798, 
(9) 
Median and Quarto-decile : 
•9694. 
It will be seen that the correlation of grade errors as thus deduced is far higher 
than when the grades are found directly from ranking. 
We now turn to the position of the grade and investigate the s.D. of its error as 
found in the two different methods by (18) and (19): 
TABLE I. Accuracy as found from Ranking and from Moments. 
n 
Grade 
Position from 
ranking 
Position from 
Mean and S.D. 
Ratio * 
•9 
1st Decile 
r7094 o-/\'A^ 
1 -3495 (T/v^iV 
1-2667 
•8 
2nd Decile 
1-4288 (t/n^V 
1-1637 o-/V^ 
1-2278 
•75 
Left Quartile 
1-3626 al^'lV 
1-1079 o-/v'A' 
1-2299 
•7 
3r(J Decile 
1-3180 o-/\']y 
1-0665 o-/v'¥ 
1-2358 
•6 
4th Decile 
1-2680 (r/s^i? 
1-0159 tr/ViV 
1-2482 
•5 
Median 
1-2533 cr/v'/V 
l-0000o-/V# 
1-2533 
•4 
6th Decile 
1-2680 (t/v'7v 
1-0159 (r/s^iV 
1-2482 
•3 
7th Decile 
1-3180 
1-0665 o-/ViV 
1-2358 
-25 
Right Quartile 
1-3626 o-js'J' 
1-1079 o-/V# 
1-2299 
•2 
8th Decile 
1-4288 a/^^W 
1-1637 a/'^W 
1-2278 
•1 
9th Decile 
1-7094 cr/v^iV' 
1-3495 o-/v'^ 
1-2667 
It will be seen that nicrease of inaccuracy at all grades is singularly nearly 
constant lying between 23 °/„ and 27 "/^ and for rough purposes may be taken as 
25 throughout the usual range of grading in deciles. 
We shall now work out two further series of values, namely a-^^-^-Xi as found 
(rt) from left to right deciles or quartiles, and (6) from the median to these grades. 
(a) Turning to (20) we put 
//. = //„and| = l-|, 
* The values in colujiins 3 and 4 were found to 6 decimals and the ratio of the s. d.'s found from 
these. Columns 3 and 4 must be multiplied by -67449 if the probable error instead of the standard 
deviation be required. 
