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.)
CHAPTER XIX.
THE THEORY OF THE AVERAGE AS A MEANS OF APPROXIMATION TO THE TRUTH.
§§ 1–4. General indication of the problem: i.e.[ TN: space] an inverse one requiring the previous consideration of a direct one.
[I. The direct problem:—given the central value and law of dispersion of the single errors, to determine those of the averages. §§ 6–20.]
6. (i) The law of dispersion may be determinable à priori,
7. (ii) or experimentally, by statistics.
8, 9. Thence to determine the modulus of the error curve.
10–14. Numerical example to illustrate the nature and amount of the contraction of the modulus of the average-error curve.
15. This curve is of the same general kind as that of the single errors;
16. Equally symmetrical,
17, 18. And more heaped up towards the centre.
19, 20. Algebraic generalization of the foregoing results.