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When the movement of a demographic variable in time is considered, a demographic time series ^{1} is obtained. It is sometimes possible to decompose a time series into a trend ^{2} around which there are fluctuations ^{3}, variations ^{3} (1411) or deviations ^{3} (1412). Where such fluctuations tend to recur after certain periods, they are called periodic fluctuations ^{4} or sometimes cyclical fluctuations ^{4}, In demography the most common period is a year, and the fluctuations in subperiods are called seasonal fluctuations ^{5}. The fluctuations that remain after trend and periodic fluctuations have been eliminated are called irregular fluctuations ^{6}. They may be due to exceptional factors, e. g. to mobilization, or sometimes they are chance fluctuations ^{7} or random fluctuations ^{7}.
151
It is occasionally desirable to replace a series of figures by another that shows greater regularity. This process is known as graduation ^{1} or smoothing ^{1}, and it generally consists of passing a regular function through a number of points of the time series or other series, such as numbers of persons by reported ages. If a freehand curve is drawn the process is known as graphic graduation ^{2}. Where analytical mathematical methods are used, this is called curve fitting ^{3}. A mathematical curve is fitted to the data, possibly by the method of least squares ^{4}, which minimizes the sum of the squares of the differences between the original and the graduated series. Other methods include moving averages ^{5} or involve the use of the calculus of finite differences ^{6}. Some of the procedures may be used for interpolation ^{7}, the estimation of values of the series at points intermediate between given values or for extrapolation ^{8}, the estimation of values of the series outside the range for which it was given,
 1. graduation n. — graduate v. — graduated adj. smoothing n. — smooth v. —smoothed adj.
 7. interpolation n. — interpolate v. — interpolated adj.
 8. extrapolation n. — extrapolate v. — extrapolated adj.
152
It is often necessary to graduate distributions to correct the tendency of people to give their replies in round numbers ^{1}. This tendency is sometimes referred to as the heaping ^{2} or bunching ^{2} of replies at preferred points ^{3}, and indices of heaping ^{4} or indices of bunching ^{4} may be constructed. One of the major applications of this method in demography is the adjustment of age distributions, where there is a tendency for people to state their ages in numbers ending with 0, 5 or other preferred digits.
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The numerical values of demographic functions are generally listed in ^{1}, such as life tables (4311), fertility tables (6341), or nuptiality tables (5221). A distinction is made between <b>current tables ^{2} which are based on observations collected during a limited period of time, and cohort tables ^{3} or generation tables ^{3}, which deal with the experience of a cohort throughout its lifetime. A similar distinction is made between current rates ^{4}, which refer to a given period of time, and cohort rates ^{5} or generation rates ^{5}, which refer to a cohort. </b>
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Where insufficient data exist to fix the value of a given variable accurately, attempts may be made to estimate ^{1} this value. The process is called estimation ^{2} and the resulting value an estimate ^{3}. Where data are practically nonexistent a conjecture ^{4} may sometimes be made to fix the variable’s order of magnitude ^{5}.
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Methods of graphic representation ^{1} or diagrammatic representation ^{1} may be used to illustrate an argument. Here the data are represented in a diagram ^{2}, graph ^{2}, figure ^{2} (cf. 1313), chart ^{3} or map ^{3}. In France the word schema is used to denote a diagram which gives a schematic ^{4} representation of a problem. Where in a diagram one coordinate axis is graduated logarithmically and the other arithmetically, the graph is called a semilogarithmic graph ^{5}, though such graphs are often inaccurately referred to as logarithmic graphs ^{5}. A true logarithmic graph ^{6} has both axes graduated logarithmically and is sometimes referred to as a double logarithmic graph ^{6}. Frequency distribution may be represented graphically by frequency polygons ^{7}, obtained by joining points representing class frequencies by straight lines, or by histograms ^{8}, where a class frequency is represented by the area of a rectangle with the class interval as its base, or by bar charts ^{9}, in which the class frequencies are proportionate to the length of a bar.
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