Bauhaus-Universität Weimar

TABLES. 
203 
Table 6. 
Values of the Probability Integral for Argument ^ ; that is, when the unit 
of measurement = the Probable error. 
Multiples 
of the 
Probable 
Error. 
•0 
T 
■2 
•3 
'4 
•5 
•6 
•7 
•s 
•9 
0 
o-oo 
0-65 
Oil 
0*16 
0-21 
0 26 
0'31 
0-36 
0-41 
' 0-46 
10 
•60 
•64 
•58 
■62 
•66 
•69 
•72 
•75 
•78 
•80 
2-0 
•82 
■84 
■86 
.88 
•89 
•91 
•92 
•93 
•94 
•95 
3-0 
•967 
.964 
•969 
•974 
•978 
•982 
■985 
•987 
•990 
•992 
4-0 
•9930 
.9943 
•9954 
•9963 
•9970 
•9976 
■9981 
•9985 
•9988 
•9990 
5-0 
•9993 
•9994 
•9996 
•9997 
•9997 
■9998 
•9993 
■9999 
•9999 
•9999 
infinite 
1-000 
Tables 5 and 6 show the proportion of eases in any Normal 
system, in -which the amount of Error lies within various extreme 
values, the total number of cases being reckoned as 1 0. Here no re¬ 
gard is paid to the sign of the Error, whether it be plus or minus, but 
its amount is alone considered. The unit of the scale by which the 
Errors are measured, differs in the two Tables. In Table 5 it is 
the ‘'Modulus,” and the result is that the Errors in one half of the 
cases, that is in 0 Ö0 of them lie within the extreme value (found by 
interpolation) of 0-4769, while the other half exceed that value. 
In Table 6 the unit of the scale is 0'4769. It is derived from Table 
5 by dividing all the tabular entries by that amount. Consequently 
one half of the cases have Errors that do not exceed TO in terms of 
the new unit, and that unit is the Probable Error of the System. 
It will be seen in Table 6 that the entry of ’50 stands opposite to 
the argument of TO. 
If it be desired to transform Tables 5 and 6 into others that shall 
show the proportion of cases in which the plus Errors and the minus 
Errors respectively lie within various extreme limits, their entries 
would have to be halved. 
Let us suppose this to have been done to Table 6, and that a 
new Table, which it is not necessary to print, has been thereby pro¬ 
duced and which we will call 6a. Next multiply all the entries in the 
new Table by 100 in order to make them refer to a total number 
of 100 cases, and call this second Table 65. Lastly make a converse 
Table to 65 ; one in which the arguments of 65 become the entries, 
and the entries of 65 become the arguments. From this the Table 7
        

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