An Introduction to the theory of statistics

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Monograph

Identifikator:: 1751730271

URN:: urn:nbn:de:zbw-retromon-127610

Document type:: Monograph

Author:: Yule, George Udny http://d-nb.info/gnd/12910504X

Title:: An Introduction to the theory of statistics

Edition:: 8. ed. rev

Place of publication:: London

Publisher:: Griffin

Year of publication:: 1927

Scope:: XV, 422 S; Ill., Diagr

Digitisation:: 2021

Collection:: Economics Books

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Chapter

Document type:: Monograph

Structure type:: Chapter

Title:: Part II. The theory of variables

Collection:: Economics Books

110 THEORY OF STATISTICS. small (¢f. Chap. VL. § 5). In this process each class-frequency is multiplied by the mid-value of the interval, the products added together, and the total divided by the number of observations. If f denote the frequency of any class, X the mid-value of the corresponding class-interval, the value of the mean so obtained may be written— 1 M= = yates : . ot 140) 8. But this procedure is still further abbreviated in practice by the following artifices:—(1) The class-interval is treated as the unit of measurement throughout the arithmetic; (2) the difference between the mean and the mid-value of some arbi- trarily chosen class-interval is computed instead of the absolute value of the mean. If 4 be the arbitrarily chosen value and X=41¢&. . . (3) ther 3(fX) =3(f.4) +3(f.9), or, since 4 is a constant, U=d+33(78) .® The calculation of 3(f.X) is therefore replaced by the calcula- tion of 3(f.£). The advantage of this is that the class-frequencies need only be multiplied by small integral numbers; for 4 being the mid-value of a class-interval, and X the mid-value of another, and the class-interval being treated as a unit, the E's must be a series of integers proceeding from zero at the arbitrary origin 4. To keep the values of £ as small as possible, 4 should be chosen near the middle of the range. It may be mentioned here that 3(£), or 3(f.¢) for the grouped distribution, is sometimes termed the first moment of the distribu- tion about the arbitrary origin 4: we shall not, however, make use of this term. 9. The process is illustrated by the following example, using the frequency-distribution of Table VIIL, Chap. VI. The arbitrary origin 4 is taken at 3-5 per cent., the middle of the sixth class-interval from the top of the table, and a little nearer than the middle of the range to the estimated position of the mean. The consequent values of ¢ are then written down as in column (3) of the table, against the corresponding frequencies, the values starting, of course, from zero opposite 3:5 per cent. Hach frequency f is then multiplied by its £ and the products entered Nr CC aoil

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