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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