Statistical Averages; A Methodological Study (Paperback)

This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated.1913 Excerpt: ... THE ARITHMETIC MEAN A. THE SIMPLE ARITHMETIC MEAN, OR, SHORTLY, ARITHMETIC MEAN 1. CONCEPT AND QUALITIES OF THE ARITHMETIC MEAN The simple arithmetic mean, the most widely known and used statistical mean, is computed by dividing the sum of the items by their number. The arithmetic mean denotes the size which the items would have if, the sum total remaining unchanged, they would all be made equally large. The statement of this value carries with it important information about the series from which the arithmetic mean was computed. From the manner of computing the arithmetic mean it 4 follows directly that the sum of the positive deviations from the arithmetic mean is equal to the sum of the. negative deviations from that mean. According to another. mathematical theorem the arithmetic mean of a series of items is characterized by the fact that the sum of the squares of the deviations of the items from the mean is a minimum. From the definition of the arithmetic mean it follows that its value will be affected by a change in any member of the series. This is not the case with other means. The median and the mode, for instance, may remain unchanged even if considerable parts of the series are changed, since these means are not computed from all the items but are found by choosing one item to represent the series because of the characteristic position of that item in the series. Therefore, median and mode can only be found in series the members of which are arranged according to magnitude. The arithmetic mean, however, does not presuppose any definite arrangement of the items and the same value is obtained by adding the items in any order. Furthermore, the arithmetic mean has this advantage over the median and the mode that it can be computed from every series of...