By Student 
10 
of advantage. If the distribution is not normal, the mean and the standard 
deviation of a sample will be positively correlated, so that although both will have 
greater variability, yet they will tend to counteract each other, a mean deviating 
largely from the general mean tending to be divided by a larger standard deviation 
Consequently I believe that the tables at the end of the present paper may be 
used in estimating the degree of certainty arrived at by the mean of a few 
experiments, in the case of most laboratory or biological work where the distribu- 
tions are as a rule of a ' cocked hat ' type and so sufficiently nearly normal. 
Section VII. Tables of 
?i — 8 n — b 
odd 
2 "1 
n even 
cos" 
Odd 
for values of n from 4 to 10 inclusive. 
V7 /•■'-■ -^^ 
Together tvith — / e dx for comparison when n = 10. 
For comparison 
?l = 4 
u = 5 
n = 0 
)i = 7 
n = 8 
n = 9 
)i = 10 

•1 
•5633 
•5745 
•5841 
•5928 
•6006 
•60787 
•61462 
■60411 
•2 
•6241 
•6458 
•6034 
•6798 
•6936 
•70705 
•71846 
■70159 
•3 
•6804 
•7096 
•7340 
•7549 
•7733 
•78961 
•80423 
•78641 
•4 
•7309 
•7657 
•7939 
•8175 
•8376 
•85465 
•86970 
•85520 
•5 
•7749 
■8131 
•8428 
•8667 
•8863 
•90251 
•91609 
•90691 
■6 
•8125 
•8518 
•8813 
•9040 
•9218 
•93600 
•94732 
•94375 
•7 
•8440 
•8830 
•9109 
•9314 
•9468 
•95851 
•96747 
•96799 
•8 
•8701 
•9076 
•9332 
•9512 
•9640 
•97328 
•98007 
•98253 
•9 
•8915 
•9269 
•9498 
•9652 
•9756 
•98279 
•98780 
•99137 
1-0 
•9092 
•9419 
•9622 
•9751 
•9834 
•98890 
•99252 
•99820 
1-1 
•9236 
•9537 
•9714 
•9821 
•9887 
•99280 
■99539 
•99926 
1-2 
•9354 
•9628 
•9782 
•9870 
•9922 
■99528 
•99713 
■99971 
1-3 
•9451 
•9700 
•9832 
•9905 
•9946 
•99688 
•99819 
■99986 
1-4 
•9531 
•9756 
•9870 
•9930 
•9962 
■99791 
•99885 
■99989 
1-5 
•9598 
•9800 
•9899 
•9948 
•9973 
•99859 
•99926 
■99999 
1-6 
•9653 
•9836 
•9920 
•9961 
•9981 
•99903 
•99951 
1-7 
•9699 
•9864 
•9937 
•9970 
•9986 
•99933 
•99968 
1-8 
•9737 
•9886 
•9950 
•9977 
•9990 
•99953 
•99978 
1-9 
•9770 
•9904 
•9959 
•9983 
•9992 
•99967 
•99985 
2-0 
•9797 
•9919 
•9967 
•9986 
•9994 
•99976 
•99990 
2-1 
•9821 
•9931 
•9973 
•9989 
•9996 
•99983 
■99993 
2-2 
•9841 
•9941 
•9978 
•9992 
•9997 
•99987 
■99995 
2-3 
•9858 
•9950 
•9982 
•9993 
•9998 
•99991 
•99996 
2-4 
•9873 
•9957 
•9985 
•9995 
•9998 
•99993 
•99997 
2-5 
•9886 
•9963 
•9987 
•9996 
•9998 
•99995 
•99998 
2-6 
•9898 
•9967 
•9989 
•9996 
•9999 
•99996 
•99999 
2-7 
•9908 
•9972 
•9991 
•9997 
•9999 
•99997 
•99999 
2-8 
•9916 
•9975 
•9992 
•9998 
•9999 
•99998 
•99999 
2-9 
•9924 
•9978 
•9993 
•9998 
•9999 
•99998 
•99999 
3-0 
•9931 
•9981 
•9994 
•9998 
•99999 
3—2 
