Estimate

“ It may also cause surprise that we ask for estimates in some cases where exact information is not immediately accessible. It may be said that statistics are misleading, but estimates are hopelessly misleading: let us have correct figures or none. That attitude is easily understood, but under the circumstances it is vain. "Correct figures," that is, meticulously exact figures, are unattainable. An estimate is in nearly all matters of daily life and business the basis, and rightly the basis, of our action. ”

“ A standard basis for the estimate is not possible because in some businesses credit is extended much more carefully than in other businesses and in some collections are followed up more vigorously than in others. In making the estimate two methods are used, one being a certain percentage of the outstanding accounts, the other being a certain percentage of the sales made during the period. ”

“ 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. ”

“ Nevertheless, it is possible for anyone, who has familiarised himself with the operations of science in one department, to comprehend the significance, and even to form a general estimate of the value, of the achievements of specialists in other departments. ”

“ I was very fond of frequenting their alleys, not only for the exercise, but because, among the various ways of estimating character, I had made up my mind that there was none more likely to be correct, than the estimate formed by the manner in which people roll the balls, especially the ladies. ”

“ Many unknown factors enter into the estimate of future incomes. The universal tendency to rhythm in motion (material or psychic) manifests itself in an overestimate or underestimate of incomes and of every other factor in value. ”

“ It cannot therefore be too forcibly repeated that an estimate is inherently but an approximation, take what care one may in its founding. While it is possible to refine mathematical calculation of averages to almost any nicety, beyond certain essentials it adds nothing to accuracy and is often misleading. ”

“ An estimate must be made of the value of the national product, and of the share which laborers receive at the time of the valuation. We will assume that all the products of society during a year can be produced by four millions of hours of the labor of an average man. The value of the yearly production equals four millions of hours. ”

“ Can we estimate the wealth of a nation by the quantity of its coin? 42It would be a curious inquiry to examine the proportion of money coined in England and in France, and to compare the quantities coined with the quantities in existence. People commonly estimate the wealth of a nation by the quantity of its coined money. ”

“ Now, in these days, when the statement that two and two make four is accepted from its latest originator as a newly discovered truth, a little extension of our mathematics, to take into our estimate people as well as things, is what we principally need, and it would be a good thing, regarded either from the point of view of what the world needs or the more selfish view of our own particular gains. ”

“ These estimates, assuming their correctness (which, so far as that quality is attainable, we generally see no reason to discredit) are indicative, doubtless, of a low and backward state. But statistics are only evidence of the present. ”

“ Those who have gathered statistics differ somewhat, some claiming one-fourth, while others put the ratio at one-sixth, one-seventh, and even as low as one-ninth. A fair estimate, and one probably very near the truth, would be one-sixth or one-seventh of the whole number. ”

“ The reader may work out results for himself on other hypotheses as to the percentage of noteworthiness among the generality. A considerably larger proportion would be noteworthy in the higher classes of society, but a far smaller one in the lower; it is to the bulk, say, to three-quarters of them, that the 1 per cent. estimate applies, the extreme variations from it tending to balance one another. ”

“ By reducing the facts to figures comparisons can easily be made and the proportion of one thing to another is more accurately presented. By divesting facts from their aspect in daily life and the caprices of temperament, a truer estimate of tendencies can be made. Because statistics generally deal with large [Pg 582] masses or great numbers, standards, ratios, and types can easily be established. The mortality statistics of insurance companies afford a good example of general averages or ratios that hold true when applied to such an uncertain proposition as the length of human life. ”

“ In order to make a preliminary estimate, before the plans of a structure are drawn, but after the general dimensions of the proposed building have been determined, architects and builders sometimes employ a method of approximate estimating, by which the cost is figured at so much per cubic foot of the building, the rate varying according to its character and the finish required. ”

“ Counting all those in and keeping on the safe side and dealing only with round figures for popular purposes we may conclude that anything from one to nine million must be deducted from our last figure to arrive at a final estimate. ”

“ With a little practice, any one can learn to take off the quantities of materials, but when it comes to determining the rates, only persons having extensive and varied knowledge of building and costs of various details can accurately estimate the time and labor required to complete the work. In order, then, that the duties and requirements of a practical estimator may be thoroughly understood, a number of detailed estimates will be given in this Section as guides. ”

“ Shall we then judge a country by the majority, or by the minority? By the minority, surely. 'Tis pedantry to estimate nations by the census, or by square miles of land, or other than by their importance to the mind of the time. ”

“ It is true that an experiment, in which the principal aim is to see what happens under certain conditions, may be regarded as an experiment of research by those who are not yet familiar with the result, but in experimental researches, strictly so called, the ultimate object is to measure something which we have already seen—to obtain a numerical estimate of some magnitude. ”

“ The value of the first, must always be estimated according to its usefulness after the modification it has received is entirely 362destroyed, and when by the nature of the thing both must be consumed together, then the total value is the sum of both. The value of the second must be estimated according to the labour it has cost to produce it. ”

“ To preserve, however, some rule in the estimation, it seems to have been the practice to keep an eye to former assessments, and to rate every man according as his ancestors, or men of such an estimated property, were accustomed to pay. ”

“ He should hear and see the estimates of workmen, and he should, as soon as he has collected the necessary facts, form estimates of his own, before he hears the calculation of others: this power of estimating will be of great advantage to gentlemen: it will circumscribe their wishes, and it will protect them against the low frauds of designing workmen. ”

“ Other experts, testifying to an aggregate, without assigning a proportion to the contributory factors, give estimates so vague as to be little more than guesses, one of them, for illustration, holding to the opinion that ten would be a fair percentage, yet unable to give a reason why the amount should not be less or greater. ”

“ These estimates have been carefully made, by practical men of undoubted character, who have brought together and embodied their information. Anxious to avoid the charge of exaggeration, they have sometimes placed their estimates below what was believed to be the actual amount of these interests. ”

“ Estimates of the national income can not be made with precision. The National Bureau of Economic Research has expressed the opinion that the margin of error in its estimates “is probably less than 10 per cent.” ”

“ We estimate the wisdom of nations by seeing what they did with their surplus capital. ”

“ Indeed, it is reasonable to use estimates at all only because the actual figures are generally not knowable in advance. However, when the actual figures do become known and they differ materially from the estimates of them previously made and they can be substituted for the estimates with almost no inconvenience or unfairness, then it seems to me to be clearly unreasonable, and hence unauthorized by § 167, to continue to rely on the estimates. ”

“ Now we simply put down a sum in the annual estimates for as many sliding-presses as are likely to be required during the ensuing financial year, introduce them wherever they seem to be necessary, and hope to go on thus for an indefinite number of years. ”

“ In most cases it would require close thought to see that the service attributed directly to them was but a reflection of that performed by some other good. Thus, more and more, the estimates placed by men on goods come to depend on knowledge and foresight, and not on immediate impressions and feelings. ”

“ Such estimates of ratios, when made by different persons, are found to vary much less than do the estimates of absolute time, and they will serve an excellent purpose whenever a satisfactory determination shall have been made of the duration of any one period. ”

“ He may say that though indefinite things do not admit of definite measurements, yet approximately true estimates of their relative values may be made when they differ considerably, and he may further say, that even when181 their relative values are not determinable, it remains true that the most valuable should be chosen. ”

“ In stating the principles which regulate exchangeable value and price, we should carefully distinguish between those variations which belong to the commodity itself, and those which are occasioned by a variation in the medium in which value is estimated, or price expressed. ”

“ Men are to be estimated, not from what they know, but from what they are able to perform; ”

“ I will add one consideration which will not have escaped those geographers who have studied the calculation of probabilities. In a series of observations made under the same circumstances, and especially by the same observers, the greater the number, the more probable is it that their amount will approach to the total quantity required. When there is no reason that the errors committed should be on one side rather than another, they mutually destroy each other, and the more so, the more the observations are multiplied. ”

“ This sphere of subjective probability is widened by the latest developments of the science [47] so far as they add to the number of constants for which it is important to determine the probable—and improbable—error. For instance, a measure of the deviation of observations from an average or mean value was required by the older writers only as subordinate to the determination of the mean, but now this “standard deviation” (below, par. 98) is often treated as an entity for which it is important to discover the limits of error. ”

“ By simple induction we know that the median of a large sample of observations is a probable value for the true median; how probable is determined as follows from a selection of our data. First suppose that all the observations are of the same weight. If x′ were the true median, the probability that as many as 1⁄2n + r of the observations should fall on either side of that point is given by the normal law for which the exponent is -2r2/n. ”

“ A mere average, therefore, might lead to conclusions only the more misleading, for their deceptive semblance of accuracy. There would be less danger of error in taking the average of only a small number of years, and correcting it by a conjectural allowance for the character of the seasons, than in trusting to a longer average without any such correction. ”

“ However, where statistical evidence is obtainable, no one dreams of estimating probability by the quantity of his belief. Insurance offices, dealing with fire, shipwreck, death, accident, etc., prepare elaborate statistics of these events, and regulate their rates accordingly. Apart from statistics, at what rate ought the lives of men aged 40 to be insured, in order to leave a profit of 5 per cent. upon £1000 payable at each man's death? Is 'quantity of belief' a sufficient basis for doing this sum? ”

“ 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. ”

“ The statistician is primarily the man of facts, not merely a recorder of facts, but one upon whom is laid the duty of their orderly arrangement, their exposition and scientific coordination. Our author inferentially recognizes these functions by mapping out a general work to bear the title of the science of the statistics. Herein will be arranged the principal contents of statistical knowledge, in two separate volumes, the one having particular reference to the needs of sociology, the other of economics. ”

“ The attempt to make comparison between the percentage of growth of population and the percentage of growth in the expenditures of the Federal Government, using no facts relative to the great increase in mechanical production and of wealth, is a vicious use of statistical data. Such showings are the results of the work of the statistical mechanic, the man who constructs statistical tables to order.
Statistics really take the place of observation. ”