The Logic of Chance, 3rd edition / An Essay on the Foundations and Province of the Theory of Probability, With Especial Reference to Its Logical Bearings and Its Application to Moral and Social Science and to Statistics

by John Venn

(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.

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.