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Multilingual Demographic Dictionary, second unified edition, English volume
14
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140
The average ^{1} or mean ^{1} most frequently used in demography is the arithmetic average ^{2} or arithmetic mean ^{2} which consists of the sum of a series of quantities divided by their number.. Where the term average or mean is used without further qualification the arithmetic average is generally meant. The geometric mean ^{3} or geometric average ^{3} is sometimes used when all observed values are positive. It is the Nth root of the product of N values. A weighted average ^{4} or weighted mean ^{4} is obtained when different items are given varying importance by multiplying each item by a particular weighting factor ^{5} or weight ^{5}. The median ^{6} is the value of the element which divides a set ^{7} of observations into two halves. The mode ^{8} is the most common or frequent value in a set of observations.
- 1. Average, n., can be used as an adjective. Mean, n., can be used as an adjective.
- 5. Weight, n. - weigh, v.
- 6. Median, n., can be used as an adjective.
- 8. Mode, n., modal, adj.
141
The dispersion ^{1}, scatter ^{1}, variation ^{1} or variability ^{1} of a set of observations depends on the differences ^{2} or deviations ^{2} between its elements. Here only the most common measures of dispersion ^{3} are mentioned. The range ^{4} is the difference between the largest and the smallest values of a set of elements. The interquartile range ^{5} is the difference between the first and the third quartiles (142-2) and contains half the observations in the set. The semi-interquartile range ^{6}, also called the quartile deviation ^{6}, which is half the interquartile range, is often taken as a measure of dispersion. The mean deviation ^{7} or average deviation ^{7} is the arithmetic mean (140-2) of the positive values of the deviations of the individual items from the average, the variance ^{8} is the arithmetic mean of the squares of these deviations and the standard deviation ^{9} is the square root of the variance.
- 9. The common notation for the standard deviation is σ.
142
If a series of observations is arranged in ascending order, values which have below them a certain proportion of the observations are referred to as quantiles ^{1} or order statistics ^{1} . The median (140-6) has been previously mentioned. Other important order statistics are the quartiles ^{2}, the deciles ^{3}, and the percentiles ^{4} or centiles ^{4}, which divide the observations into four, ten and a hundred equal parts respectively.
143
A variable is continuous ^{1} in a given interval when it can take on an infinite number of values between any two points contained in the interval. In the opposite case it is said to be discontinuous ^{2}. Where a variable can take only certain isolated values it is called a discrete ^{3} variable.
- 1. Continuous, adj. - continuity, n.
- 2. Discontinuous, adj. - discontinuity, n.
144
The arrangement of members of a population in various categories or classes of a specified attribute or variable produces a frequency distribution ^{1}, often called a distribution ^{1} for short. The ratio of the number in the individual group or cell — the absolute frequency ^{2} or class frequency ^{2} — to the total number in all groups is called the relative frequency ^{3} in that group. In demography the terms structure ^{4} and composition ^{4} are often used interchangeably to describe the distribution of characteristics such as age, sex, marital status, occupation, etc. Structure is sometimes used in a more restricted sense to describe the distribution of the population according to age and sex only.
- 4. The term population distribution usually refers to its spatial distribution. However, when used with the name of the characteristic or attribute that is analyzed, the word distribution is a synonym for structure or composition. Thus one finds references to age distribution, age and sex composition, and age and sex structure.
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