Average

“ And when we deliberately set ourselves to obtain uniformities by taking an average result, derived from comparison of a multitude of subjects, our results are, of course, always mechanical in appearance, because the element of individual purpose and initiative has been excluded by ourselves from our data in the very process of taking the average. ”

“ The process by which an average is obtained, it may be urged, insures this tendency to equalization amongst the magnitudes with which it deals. For instance, let there be a party of ten men, of whom four are tall and four are short, and take the average of any five of them. Since this number cannot be made up of tall men only, or of short men only, it stands to reason that the averages cannot differ so much amongst themselves as the single measures can. ”

“ Now when we are referring to averages it must be remembered that the minimum number of different occurrences necessary in order to justify the average is that which enables each of them to present itself once. ”

“ In dealing with masses of people—feeding them, for instance—by providing a certain average supply for each, all may be satisfied; but whenever the average is applied to individuals it is misapplied, and one finds he has too much, another that he has too little. ”

“ Where the average for a particular state for the first year is less than the general average, the per capita sum is to be increased by equal gradations, until, at the end of four years, it equals the general average. ”

“ In all calculations concerning the average rate of progress of a community, or any of its operations, the geometric mean should be employed. For if a quantity increases 100 per cent. in 100 years, it would not on the average increase 10 per cent. ”

“ Averages.—An average may be defined as a quantity derived from a given set of quantities by a process such that, if the constituents become all equal, the average will coincide with the constituents, and the constituents not being equal, the average is greater than the least and less than the greatest of the constituents. ”

“ The percentage is, of course, rarely or never precisely realised in any one year, but the longer the period of years we take for examination, the more exactly do the deviations from the average in individual years compensate one another. ”

“ That there is a difference between the average and the first-class man is known to all employers, but that the first-class man can do in most cases from two to four times as much as is done by an average man is known to but few, and is fully realized only by those who have made a thorough and scientific study of the possibilities of men. ”

“ And so if i, instead of being a particular sort of instance, is an instance known to be under the influence of a particular set of circumstances, the presumption drawn from the numerical proportions in the whole genus would probably, in such a case, only mislead. A general average should only be applied to cases which are neither known, nor can be presumed, to be other than average cases. Such averages, therefore, are commonly of little use for the practical guidance of any affairs but those which concern large numbers. ”

“ In the study of the data of 1880 I was led to the conclusion that the average per capita expenditure (and therefore the annual product in its final stage) of the people of this country for the necessaries, comforts and luxuries of life could not be less than what $200 per head could buy at the prices of the census year. The proportion of the population occupied for gain varied but a fraction from one in three, leading to the conclusion that the average product of each person occupied for gain could not be less than $600 worth a year. ”

“ One of the most approved definitions of general average is,—"All loss which arises in consequence of extraordinary sacrifices made, or expenses, incurred, for the preservation of the ship and cargo, comes within general average, and must be borne proportionately by all who are interested." ”

“ We regard the average as the result of the operation of a limited sum of forces and conditions, incalculable as regards their particular incidence, but always pressing into action, and thus likely to operate a certain number of times within a limited period. ”

“ We look on our own students as better than the average and in any case give them the benefit of the doubt. We call things 'fair' that are only average, and then the word 'fair' comes to mean average. Then we assign the grade 'fair' to students who are below the average, and a 'fair' student comes to mean a poor student. In assigning grades such words should be avoided; we should learn to think in terms of the average and probable error. ”

“ Provided only that the conditions of production remain stable, averages of large numbers will always practically present much the same general characteristics. The far more important distinction lies between the average of a few, with its fluctuating values and very imperfect and occasional attainment of its ultimate goal, and the average of many and its gradually close approximation to its ultimate value: i.e. to its objective point of aim if there happen to be such. ”

“ But if the purpose is to ascertain how a particular individual, or the average of a group of individuals, compares in particular kinds of capacity with the average or the most highly developed persons of the same status, education, occupation, or age, then the standard by which the subject must be measured must be one derived from the observation and measurement of the mental capacities of as large a number as possible of individuals engaged in all sorts of occupations and of all degrees and grades of educational attainment. ”

“ The median is often preferred to the average in psychological work, not only because it is more easily computed, but because it is less affected by the eccentric or unusual performances of a few individuals, and therefore more fairly represents the whole population. ”

“ And so the balance sways and the story runs—here a gain, there a loss, and Nature’s great average struck across the two, whereof the sum total forms one of the factors in that mighty equation in which the result will equal the unknown quantity of her purpose. ”

“ Average is a very difficult word to define. One day an Inspector asked a class what it meant. A little girl eagerly answered, 'What a hen lays eggs on.'
The Inspector was greatly surprised, but knowing that the child must have some reason for her answer, he asked her what made her think so, when she at once pointed to a sentence in her reading-book which said that 'a hen lays four or five eggs a week on an average.' The little girl evidently thought that an average was a mat or something of the kind, on which the hen deposited her eggs. ”

“ Many serious difficulties have to be overcome, and the final result must be regarded as merely approximate. For example, some observers have studied the entire population of districts; others draw their figures from the army alone, from which, of course, all the abnormally short men have been eliminated. Some give averages alone; others work by percentile grades. To be sure, these two methods give parallel results; but how discover the average from them? ”

“ It is evident, therefore, that in close-breeding, and in the crossing of varieties of different degrees of divergence, there is, first, a less than average result, then an average, then better than an average, then this better result quickly reaches a maximum and again declines, crosses the line of average and becomes bad, and finally infinitely bad, or dies out. ”

“ But these few uncommon men only serve by forming a contrast to emphasize the tendency of the average.
"This common tendency to 'take it easy' is greatly increased by bringing a number of men together on similar work and at a uniform standard rate of pay by the day. ”

“ Again, General average is the apportionment of loss caused by measures taken for the ship's safety, as cutting away the masts, throwing overboard cargo, accepting towage, or the like.—adj. containing a mean value: ordinary.—v.t. to fix an average.—v.i. to exist in, or form, a mean quantity. ”

“ The Upper Surface shows the Theoretical Distribution of Grades, the Lower that must convenient in Practise. and that ability is distributed somewhat like wages which are roughly proportional to it. If the average earnings of men in this country are $600 a year, it is clear that the positive deviations from the average are many times the negative deviations. ”

“ I. How do the self-estimates of these fifty persons agree with the judgments passed on them by their acquaintances? The following table gives, in the case of each of the nine traits studied, the average deviation of the self-estimates of the various individuals from the median position assigned them by their twenty-four associates, and [Pg 150] also the average deviation [9] among these twenty-four associates in their judgments of each individual. The figure given is in terms of the number of positions in the total scale of twenty-five possible positions. ”

“ The normal rate seems to refer to the actual conditions of industry, the rate which can be obtained for a given amount of exertion, taking the average of employments at the time, rather than to the particular rate obtained for some class of work over a period of years. ”

“ On special occasions, such as opening days, it is said to have reached fifty thousand, but the general average is placed at fifteen thousand, and they represent every grade in life. Rich and poor mingle here freely. ”

“ Take another set of ten throws, and we may get another average, say four. There is clearly nothing objective peculiarly corresponding in any way to these averages. No doubt if we go on long enough we shall find that the averages tend to centre about 3.5: we then call this the average, or the ‘probable’ number of points; and this ultimate average might have been pretty constantly asserted beforehand from our knowledge of the constitution of a die. It has however no other truth or reality about it of the nature of a type: it is simply the limit towards which the averages tend. ”

“ Он — среднего роста. He's of medium height. • average. Он человек средних способностей. He's a man of average ability. — Какая у вас на заводе средняя зарплата? What's the average pay at your factory? • just fair. Урожай у нас в этом году средний. Our harvest this year is just fair.
□ в среднем on an average. Я работаю в среднем по девять часов в день. I work on an average of nine hours a day. ”

“ It gives, in short, the average tint of every unit of area in the picture, measured from the fiducial lines as co-ordinates. Now every statistician knows, by experience, that numerical averages usually begin to agree pretty fairly when we deal with even twenty or thirty cases. Therefore we should expect to find that any groups of twenty or thirty men of the same class would yield composites bearing a considerable likeness to one another. ”

“ Thus if in the first of the averages above instanced (the arithmetic mean) the constituent xr, occurs l times, the expression is to be modified by putting lxr for xr in the numerator, and in the denominator, for n, n+r−1. The definition of an average covers a still wider held. The process employed need not be a function. [156] One of the most important averages is formed by arranging the constituents in the order of magnitude and taking for the average a value which has as many constituents above it as below it, the median. ”

“ As regards the second point, the raising of the average as opposed to the upper level of attainment, not much need be said. That part of our civilization which can be thought of as progressive is largely concerned with this very thing—with making it possible for men to realize in larger measure their inherent possibilities. ”

“ In the absence of sufficiently complete data, it is not easy, and perhaps not possible, to estimate accurately, and specifically state the average saving in time and labor in the world's work of production and distribution that has been thus achieved. ”

“ There are many people of average weight or nearly so, but few people who deviate widely from the average weight. If we measure people with refer ence to any other physical characteristic, or any mental characteristic, we get a similar result, we find them grouped about an average or central tendency. ”

“ In asymmetrical curves of error the arithmetic average must he distinguished from, 5. (3) the Maximum Ordinate average, 6. (4) and the Median. 7. Diagram in illustration. 8—10. Average departure from the average, considered under the above heads, and under that of 11. (5) The (average of) Mean Square of Error. 12—14. The objects of taking averages. 15. Mr Galton's practical method of determining the average, 16, 17. No distinction between the average and the mean. 18—20. Distinction between what is necessary and what is experimental here. ”

“ If the income distribution remains the same (all incomes grow with the same rate) then also the average income, y = W grows at the same rate, and then also the net income distribution remains the same, and then the ratio of net average to subsistence remains the same too. ”

“ "Of course schools are made for the average. The holes are all round, and whatever shape the pegs are they must wedge in somehow. One hasn't time to bother about anything but the average." ”

“ The new education, he contends, recognizes the absurdity of averaging unlike quantities, and accepts the ultimate truth that each child is an individual, differing in needs, capacity, outlook, energy, and enthusiasm from every other child. An arithmetic average can be struck, but when it is applied to children it is a hypothetical and not a real quantity. There is not, and never will be, an average child ”

“ You've seen an unemployment rate that was well below the national average 12 months ago now being well, well above -- almost twice what the national average is -- is twice what the national average is. ”