CONTENTS, 
CHAPTER XV. 
THE BINOMIAL DISTRIBUTION AND THE 
NORMAL CURVE. 
1-2. Determination of the frequency-distribution for the number . 
of successes in n events: the binomial disiribution—3. 
Dependence of the form of the distribution on p, ¢, and n— 
4-5. Graphical and mechanical methods of forming re- 
presentations of the binomial - distribution—6. Direct 
calculation of the mean and the standard-deviation from 
the distribution—7-8. Necessity of deducing, for use in 
many practical cases, a continuous curve giving approxi- 
mately, for large values of n, the terms of the binomial 
series—9. Deduction of the normal curve as a limit to the 
symmetrical binomial—10-11. The value of the central 
ordinate—12. Comparison with a binomial distribution for 
a moderate value of n—18. Outline of the more general 
conditions from which the curve can be deduced by advanced 
methods—14. Fitting the curve to an actual series of 
observations—15. Difficulty of a complete test of fit by 
elementary methods—16. The table of areas of the normal 
curve and its use—17. The quartile deviation and the 
¢¢ probable error ’—18. Illustrations of the application of 
the normal curve and of the table of areas . . 291-316 
CHAPTER XVL 
NORMAL CORRELATION. 
1-3. Deduction of the general expression for the normal correlation 
surface from the case of independence—4. Constancy of the 
standard-deviations of parallel arrays and linearity of the 
regression—5. The contour lines : a series of concentric and 
similar ellipses—6. The normal surface for two correlated 
variables regarded as a normal surface for uncorrelated vari- 
ables rotated with respect to the axes of measurement: 
arrays taken at any angle across the surface are normal 
distributions with constant standard-deviation : distribution 
of and correlation between linear functions of two normally 
correlated variables are normal : principal axes—7. Standard- 
deviations round the principal axes—8-11. Investigation of 
Table III., Chapter IX., to test normality: linearity of 
regression, constancy of standard-deviation of arrays, 
normality of distribution obtained by diagonal addition, 
contour lines—12-13. Isotropy of the normal distribution 
for two variables—14. Outline of the principal properties of 
the normal distribution for n variables  . , 317-334 
X1V 
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