Page:Logic of Chance (1888).djvu/28

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xxviii

Contents.

§19, 20.	Combination of testimony.
21, 22.	Scientific meaning of a miracle.
23, 24.	Two distinct prepossessions in regard to miracles, and the logical consequences of these.
25.	Difficulty of discussing by our rules cases in which arbitrary interference can be postulated.
26, 27.	Consequent inappropriateness of many arguments.

CHAPTER XVIII.
ON THE NATURE AND USE OF AN AVERAGE, AND ON THE DIFFERENT KINDS OF AVERAGE.
§ 1.	Preliminary rude notion of an average,
2.	More precise quantitative notion, yielding (1) the Arithmetical Average,
3.	(2) the Geometrical
4.	In asymmetrical curves of error the arithmetic average must he distinguished from,
5.	(3) the Maximum Ordinate average,
6.	(4) and the Median.
7.	Diagram in illustration.
8—10.	Average departure from the average, considered under the above heads, and under that of
11.	(5) The (average of) Mean Square of Error.
12—14.	The objects of taking averages.
15.	Mr Galton's practical method of determining the average,
16, 17.	No distinction between the average and the mean.
18—20.	Distinction between what is necessary and what is experimental here.
21, 22.	Theoretical defects in the determination of the 'errors'.
23.	Practical escape from these.
(Note about the units in the exponential equation and integral.)

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