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 II. The theory of variables

Collection:: Economics Books

14¢ THEORY OF STATISTICS. venience, be taken as origin. Thus in Example ii. the median is (Chap. VIL § 15) 3-195 per cent. Hence 3:0 per cent. should be taken as the origin, d = + 0-39 intervals, NV; = 327, /,= 305. The deviation-sum with 3'0 as origin is found to be 1263, and the correction is +039 x 22= +86. Hence the mean deviation from the median is 2:012 intervals, or again 1:01 per cent. The value is really smaller than that of the mean deviation from the arithmetic mean, but the difference is too slight to affect the second place of decimals. It should be noted that, as in the case of the standard deviation, this method of calculation implies the assumption that all the values of X within any one class-interval may be treated as if they were the mid-value of that interval. This is, of course, an approximation; but as a rule gives results of amply sufficient accuracy for practice if the class-interval be kept reasonably small (¢f. again Chap. VI. § 5). We have left it as an exercise to the student to find the correction to be applied if the values in each interval are treated as if they were evenly distributed over the interval, instead of concentrated at its centre (Question 7). 18. The mean deviation, it will be seen, can be calculated rather more rapidly than the standard deviation, though in the case of a grouped distribution the difference in ease of calculation is not great. It is not, on the other hand, a convenient magnitude for algebraical treatment ; for example, the mean deviation of a dis- tribution obtained by combining several others cannot in general be expressed in terms of the mean deviations of the component distributions, but depends upon their forms. As a rule, it is more affected by fluctuations of sampling than is the standard deviation, but may be less affected if large and erratic deviations lying somewhat beyond the bulk of the distribution are liable to occur. This may happen, for example, in some forms of experimental work, and in such cases the use of the mean deviation may be slightly preferable to that of the standard deviation. 19. It is a useful empirical rule for the student to remember that for symmetrical or only moderately asymmetrical distri- butions, approaching the ideal forms of figs. 5 and 9, the mean deviation is usually very nearly four-fifths of the standard devia tion. Thus for the distribution of pauperism we have mean deviation 1-01 0-81 standard deviation 1:24 ~~ °° In the case of the distribution of male statures in the British Isles, Example iii., the ratio found is 0:80. For a short series of observations like the wage statistics of Example i. a regular result could hardly be expected: the actual ratio is 15°0/20'5=0-73. 0

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