Grundzüge der Sozialpolitik

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Monograph

Identifikator:: 876559135

URN:: urn:nbn:de:zbw-retromon-1676

Document type:: Monograph

Author:: Borght, Richard van der http://d-nb.info/gnd/11625274X

Title:: Grundzüge der Sozialpolitik

Place of publication:: Leipzig

Publisher:: Verlag von C. L. Hirschfeld

Year of publication:: 1904

Scope:: 1 Online-Ressource (XII, 566 Seiten)

Digitisation:: 2017

Collection:: Economics Books

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Document type:: Monograph

Structure type:: Chapter

Title:: I.Teil. Allegeines

Collection:: Economics Books

VIL. —AVERAGES. 109 or, to express it more briefly by using the symbol 3 to denote “the sum of all quantities like,” 1 M= 7 2(&) 2 (1) The word mean or average alone, without qualification, is very generally used to denote this particular form of average: that is to say, when anyone speaks of ‘the mean” or “the average” of a series of observations, it may, as a rule, be assumed that the arithmetic mean is meant. It is evident that the arithmetic mean fulfils the conditions laid down in (a) and (8) of § 4, for it is rigidly defined and based on all the observations made. Further, it fulfils condition (c), for its general nature is readily comprehensible. If the wages-bill for & workmen is £P, the arithmetic mean wage, P/N pounds, is the amount that each would receive if the whole sum available were divided equally between them : conversely, if we are told that the mean wage is £M, we know this means that the wages-bill is VV. pounds. Similarly, if & families possess a total of C children, the mean number of children per family is C'/N—the number that each family would possess if the children were shared uniformly. Conversely, if the mean number of children per family is 27, the total number of children in A families is #.4#. The arithmetic mean expresses, in fact, a simple relation between the whole and its parts. 7. As regards simplicity of calculation, the mean takes a high position. In the cases just cited, it will be noted that the mean is actually determined without even the necessity of determining or noting all the individual values of the variable: to get the mean wage we need not know the wages of every hand, but only the wages-bill ; to get the mean number of children per family we need not know the number in each family, but only the total. If this total is not given, but we have to deal with a moderate number of observations—so few (say 30 or 40) that it is hardly worth while compiling the frequency-distribution—the arithmetic mean is calculated directly as suggested by the definition, z.e. all the values observed are added together and the total divided by the number of observations. But if the number of observations be large, this direct process becomes a little lengthy. It may be shortened considerably by forming the frequency-table and treating all the values in each class as if they were identical with the mid-value of the class-interval, a process which in general gives an approximation that is quite sufficiently exact for prac- tical purposes if the class-interval has been taken moderately vl

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