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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 (141-1) or deviations 3 (141-2). 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 sub-periods 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.
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 free-hand 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.
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.
The numerical values of demographic functions are generally listed in 1, such as life tables (431-1), fertility tables (634-1), or nuptiality tables (522-1). 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>
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 non-existent a conjecture 4 may sometimes be made to fix the variable’s order of magnitude 5.
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. 131-3), 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 co-ordinate axis is graduated logarithmically and the other arithmetically, the graph is called a semi-logarithmic 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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