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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Document type:: Monograph

Structure type:: Chapter

Title:: Part III. Theory of sampling

Collection:: Economics Books

THEORY OF STATISTICS. can be drawn freehand, or by aid of a curve ruler, through the tops of the ordinates so determined. The logarithms of # in the table on p. 303 are given to facilitate the multiplication. The only point in which the student is likely to find any difficulty is in the use of the scales: he must be careful to remember that the standard-deviation must be expressed in terms of the class-interval as a wnat in order to obtain for y, a number of observations per interval comparable with the frequencies of his table. The process may be varied by keeping the normal curve drawn to one scale, and redrawing the actual distribution 80 as to make the area, mean, and standard-deviation the same. Thus suppose a diagram of a normal curve was printed once for all to a scale, say, of y,=5 inches, o=1 inch, and it were required to fit the distribution of stature to it. Since the standard-deviation is 2-57 inches of stature, the scale of stature is 1 inch =2'57 inch of stature, or 0:389 inches =1 inch of stature ; this scale must be drawn on the base of the normal-curve diagram, being so placed that the mean falls at 67-46. As regards the scale of frequency-per-interval, this is given by the fact that the whole area of the polygon showing the actual distribution must be equal to the area of the normal curve, that is 5 «/2r=1253 square inches. If, therefore, the scale required is n= observations per interval to the inch, we have, the number of observations being 8585, 8585 nx 2:57 RRs which gives n= 266-6. Though the second method saves curve drawing, the first, on the whole, involves the least arithmetic and the simplest plotting. 15. Any plotting of a diagram, or the equivalent arithmetical comparison of actual frequencies with those given by the fitted normal distribution, affords, of course, in itself, only a rough test, of a practical kind, of the normality of the given distribution. The question whether all the observed differences between actual and calculated frequencies, taken together, may have arisen merely as fluctuations of sampling, so that the actual distribution may be regarded as strictly normal, neglecting such errors, is a question of a kind that cannot be answered in an elementary work (cf. ref. 22). At present the student is in a position to compare the divergences of actual from calculated frequencies with fluctuations of sampling in the case of single class-intervals, or single groups of class-intervals only. If the 308

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