Indicator diagram

“ The number of letters per word were used as abscissas, the number of words per thousand containing a definite number of letters were taken for ordinates, and the resulting points connected by straight lines. Thus a graph or diagram was obtained which presents to the eye in a simple manner the relative frequencies of words of different lengths. Two such diagrams from the same author will agree more or less closely, depending upon the number of words in the groups upon which the averages are based. ”

“ The ratio of any element of area in the volume-pressure or the entropy-temperature diagram, or in any other in which the scale of work and heat is unity, to the corresponding element in the volume-entropy diagram is represented by or The cases in which this ratio is 0, or changes its sign, demand especial attention, as in such cases the diagrams of constant scale fail to give a satisfactory representation of the properties of the body, while no difficulty or inconvenience arises in the use of the volume-entropy diagram. ”

“ It will be noticed that in the diagram the three lines, especially those of Price and Consumption (which may be considered natural resultants, in contrast with the arbitrary fixation of a Tax) , do not depart widely from regular curves; and accordingly, assuming the causes at work to vary continuously during the intervals between points of measurement, curves may be substituted. In fact, a curve often represents the course of a phenomenon more truthfully than can be done by a line that zigzags along the exact measurements ”

“ The different diagrams which we obtain by different laws of association are all such as may be obtained from one another by a process of deformation, and this consideration is sufficient to demonstrate their properties from the well-known properties of the diagram in which the volume and pressure are represented by rectangular co-ordinates. ”

“ A pointer or indicator is provided which is pivoted at F and has one extensional arm resting against the pin A, which is pointed in order to secure a line contact. At the end of the indicator a small scale is graduated with the zero mark in the center, and as the indicator swings to one side or the other the variations in the size of the piece measured are easily determined. ”

“ On return the indicator number is simply turned round, and the borrower receives back his card. “Overdues” can be shown by means of coloured clips, or by having the borrowers’ cards shaped or coloured, and issues are recorded on day-sheets, or by means of application forms. There are, however, endless ways of working both the Elliot and Cotgreave indicators, though there is only space to describe the most elementary forms. Like every other department of library work, the working of an indicator-charging system will bear careful thought, and leave room for original developments. ”

“ The method of representation, in which the co-ordinates of the point in the diagram are made equal to the volume and entropy of the body, presents certain characteristics which entitle it to a somewhat detailed consideration, and for some purposes give it substantial advantages over any other method. ”

“ The plans and designs drawn by architects and engineers are used to determine the value of certain real magnitudes by measuring certain distances on the diagram. For such purposes it is essential that the drawing be as accurate as possible. ”

“ You proceed in the same way until all the counters are placed. Remember you always touch a vacant place and slide the counter from it to the next place, which must be also vacant. Now, by the "buttons and string" method of simplification we can transform the diagram into E. Then the solution becomes obvious. "Always move to the point that you last moved from." This is not, of course, the only way of placing the counters, but it is the simplest solution to carry in the mind. ”

“ The latter cycle in this case includes in it the varying cycle.
On inspecting the ten Working-Variables of the diagram, it will be perceived, that although the value on any one of them (excepting and ) goes through a series of changes, the office which each performs is in this calculation fixed and invariable. Thus always prepares the numerators of the factors of any ; the denominators. always receives the th factor of , and the th. always decides which of two courses the succeeding processes are to follow, by feeling for the value of through means of a subtraction ”

“ Copy the simple diagram, enlarged, on a sheet of paper; then place two white counters on the points 1 and 2, and two red counters on 9 and 10, The puzzle is to make the red and white change places. You may move the counters one at a time in any order you like, along the lines from point to point, with the only restriction that a red and a white counter may never stand at once on the same straight line. ”

“ An indicator is a device for indicating or registering information about books, in such a way that it can be seen either by the staff alone, or by the public and staff both. The information usually conveyed to the public is some kind of indication of the presence or absence of books, and the methods of accomplishing this almost invariably take the form of displayed numbers, qualified in such a way as to indicate books in and out. ”

“ We have now to mark the two positive portions, "some are " and "some are ".
The only two compartments, available for Things which are , are No. 9 and No. 10. Of these, No. 9 is already marked as 'empty'; so our red counter must go into No. 10.
Similarly, the only two, available for , are No. 11 and No. 13. Of these, No. 11 is already marked as 'empty'; so our red counter must go into No. 13.
The final result is
And now how much of this information can usefully be transferred to the smaller Diagram? ”

“ The lines dividing the lots, instead of running perpendicularly according to the diagram, actually run diagonally, the effect of which is necessarily to displace the whole of the lots, upwards of 300 in number, from their true position. The lines dividing the ranges are so irregular as to give to some lots two and a half times the contents of others, though they are all laid down in the diagram as of equal extent ”

“ These graphs represent the normal form of distribution usually expected when any fundamental ability is measured in a random group. If the number of cases at each unit of measurement are plotted by a point placed relatively as far above the scale, used as a base line, as the number of cases found at that unit of the scale, it will be discovered that these points arrange themselves in the form of a symmetrical curve high at the middle and flaring out 257along the base-line scale. ”

“ In the following theorems we suppose, as always, that the systems forming an ensemble are identical in nature and in the values of the external coördinates, which are here regarded as constants.
Theorem I. If an ensemble of systems is so distributed in phase that the index of probability is a function of the energy, the average value of the index is less than for any other distribution in which the distribution in energy is unaltered. ”

“ These are the principal points in the three best indicators yet [32] invented, and it only remains to note their differences. The Elliot indicator system makes the charge to the borrower, and preserves no permanent record of book issues apart from the label in the book itself. The Cotgreave system charges the borrower to the book, and does keep a permanent record of the issues. ”

“ The requirements of an index and the proportions of its several parts are the two principal questions to be considered. Under the first head it may be observed that the index of a company upon a large scale should afford as much abstract information as possible. Those who refer to it do so with different views, for the objects of their inquiry must necessarily vary with their respective duties. It is therefore desirable that the index should be constructed with a view to provide for the wants of each person, so far, at least, as to enable him to obtain information in the most direct way ”

“ Whether your data can be suitably represented by a stem and leaf display depends on whether they can be rounded without loss of important information. Also, their extreme values must fit into two successive digits, as the data in Figure 5 fit into the 10,000 and 100,000 places (for leaves and stems, respectively) . Deciding what kind of graph is best suited to displaying your data thus requires good judgment. Statistics is not just recipes! ”

“ The diagram was, however, so destitute of all credibility, that neither these easily deceived women, nor the most rustic class of men, nor those who were ready to be led away by any plausible pretender whatever, ever gave their assent to the diagram. Nor, indeed, have we ever met any individual, although we have visited many parts of the earth, and have sought out all those who anywhere made profession of knowledge, that placed any faith in this diagram. ”

“ Why are we so interested in the type of scale that measures a dependent variable? The crux of the matter is the relationship between the variable's level of measurement and the statistics that can be meaningfully computed with that variable. ”

“ In general in chart preparation the scale should be restricted to the minimum that can be used to fulfill the particular object and clearly represent what is desired. A chart of very large scale is not convenient for plotting, and a moving vessel may pass quickly beyond it or into range of objects beyond the limits of the chart. ”

“ Each individual manager selects the particular set of facts which he thinks will best show the trend of the business. The complexity of the business usually determines the number of reports.
Use of Graphs in the Presentation of Statistics
Chart Showing Comparison of Sales
with Cost of Advertising
Long experience or special aptitude may qualify a man to grasp readily the full significance of statistical compilations in a variety of forms without the use of charts or graphs. ”

“ If we represent the corresponding value of u by an ordinate drawn from the line, the extremities of all such ordinates will lie on a curve which will be the graph of u with regard to x. Interpolation therefore consists in determining the length of the ordinate of a curve occupying a particular position, when the lengths of ordinates occupying certain specified positions are known. If u is a function of two variables, x and y, we may similarly represent it by the ordinate of a surface, the position of the ordinate being determined by the values of x and of y jointly. ”

“ The twenty-four maps or charts which bear especially on American conditions have been inserted in order the better to apply principles to the state of things directly about us. This method is of great importance. As many kinds of graphic representation as possible have been introduced. No other text-book on political economy exists which makes use of charts in this way. It both interests the pupil and makes statistics alive, and it stimulates a reader to a study of facts and to the verification of economic principles. ”

“ Theorem VII. If a system which in its different phases constitutes an ensemble consists of two parts, and we consider the average index of probability for the whole system, and also the average indices for each of the parts taken separately, the sum of the average indices for the parts will be either less than the average index for the whole system, or equal to it, but cannot be greater. The limiting case of equality occurs when the distribution in phase of each part is independent of that of the other, and only in this case. ”

“ Similarly with the measurements of the ancient buildings. In this case if all our various ‘errors’ were thrown together into one group of statistics we should find that the resultant curve of facility displayed, not two peaks only, but a succession of them; and these of various magnitudes, corresponding to the frequency of occurrence of each particular measurement. We might take an average of the whole, but hardly any rational purpose could be subserved in so doing; whereas each separate point of maximum frequency of occurrence has something significant to teach us. ”

“ To address the question of the maximum potential of the COALS, ESA, WLM, and W3C3 models for correlation with human ratings, an oracle analysis was undertaken [73] . The oracle first converts the output of each model to ranks. Then for each word pair, the oracle selects the output of the model whose rank most closely matches the rank of the human rating. This procedure generates the best possible correlation with the human ratings, based on the assumption that the oracle will choose the closest model output every time. ”

“ The bias and imprecision of the source measurements can be differentially affected by intermediate operations in producing the final estimate. For example, if the final estimate is a function of a single average of many source measurements, its bias is not affected by the averaging while imprecision is reduced as a function of the square root of the number of measurements. ”

“ We have also shown that the average square of the anomalies of , that is, of the deviations of the individual values from the average, is in general of the same order of magnitude as the reciprocal of the number of degrees of freedom, and therefore to human observation the individual values are indistinguishable from the average values when the number of degrees of freedom is very great. ”