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When the movement of a demographic variable in time is considered, a demographic time series1 is obtained. It is sometimes possible to decompose a time series into a trend2 around which there are fluctuations3, variations3 (141-1) or deviations3 (141-2). Where such fluctuations tend to recur after certain periods, they are called periodic fluctuations4 or sometimes cyclical fluctuations4, In demography the most common period is a year, and the fluctuations in sub-periods are called seasonal fluctuations5. The fluctuations that remain after trend and periodic fluctuations have been eliminated are called irregular fluctuations6. They may be due to exceptional factors, e. g. to mobilization, or sometimes they are chance fluctuations7 or random fluctuations7.
It is occasionally desirable to replace a series of figures by another that shows greater regularity. This process is known as graduation1 or smoothing1, 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 graduation2. Where analytical mathematical methods are used, this is called curve fitting3. A mathematical curve is fitted to the data, possibly by the method of least squares4, which minimizes the sum of the squares of the differences between the original and the graduated series. Other methods include moving averages5 or involve the use of the calculus of finite differences6. Some of the procedures may be used for interpolation7, the estimation of values of the series at points intermediate between given values or for extrapolation8, 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 numbers1. This tendency is sometimes referred to as the heaping2 or bunching2 of replies at preferred points3, and indices of heaping4 or indices of bunching4 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 tables2 which are based on observations collected during a limited period of time, and cohort tables3 or generation tables3, which deal with the experience of a cohort throughout its lifetime. A similar distinction is made between current rates4, which refer to a given period of time, and cohort rates5 or generation rates5, which refer to a cohort. </b>
Where insufficient data exist to fix the value of a given variable accurately, attempts may be made to estimate1 this value. The process is called estimation2 and the resulting value an estimate3. Where data are practically non-existent a conjecture4 may sometimes be made to fix the variable’s order of magnitude5.
Methods of graphic representation1 or diagrammatic representation1 may be used to illustrate an argument. Here the data are represented in a diagram2, graph2, figure2 (cf. 131-3), chart3 or map3. In France the word schema is used to denote a diagram which gives a schematic4 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 graph5, though such graphs are often inaccurately referred to as logarithmic graphs5. A true logarithmic graph6 has both axes graduated logarithmically and is sometimes referred to as a double logarithmic graph6. Frequency distribution may be represented graphically by frequency polygons7, obtained by joining points representing class frequencies by straight lines, or by histograms8, where a class frequency is represented by the area of a rectangle with the class interval as its base, or by bar charts9, in which the class frequencies are proportionate to the length of a bar.
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