An Introduction to the theory of statistics

Bibliographic data

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

VL—THE FREQUENCY-DISTRIBUTION. 7) The numbers of rays range from 6 to 20,—12, 13, or 14 rays being the most usual. 4. To expand slightly the brief description given in § 2, tables like the preceding are formed in the following way :—(1) The magnitude of the class-interval, 7.e. the number of units to each interval, is first fixed ; one unit was chosen in the case of Tables I. and IIL, five units in the case of Table II. (2) The position or origin of the intervals must then be determined, e.g. in Table I. we must decide whether to take as intervals 12-13, 13-14, 14-15, ete, or 125-135, 13-5-14'5, 14'5-15'5, ete. (3) This choice having been made, the complete scale of intervals is fixed, and the observations are classified accordingly. (4) The process of classification being finished, a table is drawn up on the general lines of Tables I.-III., showing the total numbers of observations in each class-interval. Some remarks may be made on each of these heads. 5. Magnitude of Class-Interval.—As already remarked, in cases where the variation proceeds by discrete steps of considerable magnitude as compared with the range of variation, there is very little choice as regards the magnitude of the class-interval. The unit will in general have to serve. But if the variation be con- tinuous, or at least take place by discrete steps which are small in comparison with the whole range of variation, there is no such natural class-interval, and its choice is a matter for judgment. The two conditions which guide the choice are these: (a) we desire to be able to treat all the values assigned to any one class, without serious error, as if they were equal to the mid-value of the class-interval, e.g. as if the death-rate of every district in the first class of Table I. were exactly 13-0, the death-rate of every district in the second class 140, and so on; (2) for con- venience and brevity we desire to make the interval as large as possible, subject to the first condition. These conditions will generally be fulfilled if the interval be so chosen that the whole number of classes lies between 15 and 25. A number of classes less than, say, ten leads in general to very appreciable inaccuracy, and a number over, say, thirty makes a somewhat unwieldy table. A preliminary inspection of the record should accordingly be made and the highest and lowest values be picked out. Dividing the difference between these by, say, five and twenty, we have an approximate value for the interval. The actual value should be the nearest integer or simple fraction. 6. Position of Intervals.—The position or starting-point of the intervals is, as a rule, more or less indifferent, but in general it is fixed either so that the limits of intervals are integers, or, as in Tables I. and II., so that the mid-values are integers. It may, AE)

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