An Introduction to the theory of statistics

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Monograph

Identifikator:: 1757028552

URN:: urn:nbn:de:zbw-retromon-135495

Document type:: Monograph

Title:: The agricultural output of England and Wales 1925

Place of publication:: London

Publisher:: Stat. Off.

Year of publication:: 1927

Scope:: XV, 152 Seiten; graph. Darst., Kt.

Digitisation:: 2021

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: Chapter III. The production of crops

Collection:: Economics Books

170 THEORY OF STATISTICS. might be to all the points. But sucha method is hardly satis- factory, more especially if the points are somewhat scattered ; it leaves too much room for guesswork, and different observers obtain very different results. Some method is clearly required which will enable the observer to determine equations to the two lines for a given distribution, however irregularly the means may lie, as simply and definitely as he can calculate the means and standard deviations. 10. Consider the simplest case in which the means of rows lie CES » 3d Fic. 34. exactly on a straight line ER (fig. 34). Let JM, be the mean value of ¥, and let RR cut Myx, the horizontal through M/,, in A. Then it may be shown that the vertical through J/ must cut OX in M,, the mean of X. For, let the slope of RR to the vertical, i.e. the tangent of the angle MMR or ratio of 4l to IM, be b,, and let deviations from My, Mx be denoted by » and y. Then for any one row of type y in which the number of observations is n, S (x) =n.byy, and therefore for the whole table, since 2(ny)=0, S(x)=b,3(ny) = 0. 1M; must therefore be the mean of X, and JI may accordingly be termed the mean of the whole distribution. Knowing that RE passes through M, it remains only to determine @® LC

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