120 On the Prohahle Errors of Frequency Constants 
by V2. But the figures deduced in this way from the fifth column of Table III 
have for multipliers of (t/\/2N 
1-36G0, 1-G036, 17887, 2-0406, 3-0150 
instead of the multipliers 
1-2570, 1-4702, 1 6495, 1-8999, 2-8897 
TABLE III. Accuracy of Determination of a from Asipnnietrical Ranks. 
Range x-^ - x ? 
O'er from i^j-i-x, 
From Mean and S.D. 
'0 
-5 
"5 
"5 
-5 
•1 
-2 
•25 
-3 
-4 
1-28155 0- 
•84162 o- 
-67449 0- 
-52440 a 
-25335 a 
2-4757 a/s'^N' 
1-9087 alJiW 
1-7062 o-/v^2iV 
1-5134 (t/\'2N 
1-0803 aj^^^' 
1- 9318 0-/V2J' 
2- 2678 0-/V2A' 
2-5296 (r/V2# 
2-8859 a•/^/2iV■ 
4-2639 o-/s''2^ 
The S.I), of the ranges 
will be the coeffici- 
ents of column 3 x 
a-/^2N. The S.D. 
of the S.D. will be 
throughout (r/JilY 
-9 
-3 
1 -80595 a 
2-7114 o-/v^27\"^ 
1-5014 (tI\^¥F 
•8 
-1 
2-02317 0- 
2-8808 o-/v^2iV' 
1-4239 (t/v''2# 
-9 
1 
2-74680 0- 
3-4327 G-l^fM 
1-2J97 <7/v'2i7 
-9 
1 
■2 0 
2-92643 0- 
3-6974 a/s^M 
1-2634 o-/V2i\^ 
of the last five entries of the fourth column of the table on p. 119. The explanation 
of this result is the relatively high correlation between a\ and which reduces the 
higher values above resulting from a supposed independence of errors in the deter- 
mination of our two quartile distances. Physically this signifies that if we were to 
determine one median to quartile distance from a first sample of N, and the other 
median to quartile distance from a second sample, we should get a less accurate 
result than determining both quartiles on the 'same sample. For the principle of 
correlation shows us that in the same sample if we get an excess in one quartile 
distance we shall on the average get a defect in the other. We thus may actually 
lose in accuracy when we combine measurements drawn from difterent samples in 
estimating the constants of a sampled population. 
(4) The next (juestion to be raised is whether the median can be obtained more 
accurately than by halving our total frequency. We have seen that the error of 
this process is 1 -25330-/ ViV". We might, however, obtain it as the half of any two 
grades on either side the median at equal distances from it, i.e. 
7n = 2- (xi + a-'a). 
Let each of the grades cut off Hj from the tails of the frequency, then 
= {_} 'li /'i _ _JL "1 !iir^ 
'^yh 
