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The average1 or mean1 most frequently used in demography is the arithmetic average2 or arithmetic mean2 which consists of the sum of a number 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 mean3 or geometric average3 is sometimes used to estimate the total population in the middle of a period for which the population at either end is given; it is the square root of the product of the two end populations, A weighted average4 or weighted mean4 is obtained when different items are given varying importance by multiplying each item by a particular weight5. The median6 is the value of the element which divides a set7 of observations into two halves. The mode8 is the most common or most frequent value of a set of observations
- 8. mode n. — modal adj.
The dispersion1, scatter1, variation1 (150-3) or variability1 of a set of observations depends on the differences2 or deviations2 (150-3) between its elements, Here the most common measures of dispersion3 only are mentioned. The range4 is the difference between the largest and the smallest value of a set of elements. The interquartile range5 is the difference between the first and third quartiles (cf. paragraph 142) and contains half the observations of the set. The semi-interquartile range6, also called the quartile deviation6, which is half the interquartile range, is often taken as a measure of dispersion. The mean deviation7 or average deviation7 is the arithmetic mean (140-2) of the positive values of the deviations of individual items from the average, the variance8 is the arithmetic mean of the squares of these deviations and the standard deviation9 is the square root of the variance.
- 9. The common notation for the standard deviation is σ,
If a series of observations is arranged in ascending order, values which have below them a certain proportion of the observations are called quantiles1 or order statistics1. The median (140-6) has already been mentioned. Other important order statistics are the quartiles2, the deciles3 and the percentiles4 or, centiles4, which divide the population into four, ten and a hundred equal parts respectively.
A variable is continuous1 in a given interval when it can take an infinity of values between any two points contained in the interval. In the opposite case it is said to be discontinuous2. Where a variable can take only certain isolated values it is called a discrete3 variable.
- 1. continuous adj. — continuity n.
- 2. discontinuous adj. — discontinuity n.
The arrangement of members of a population in various categories or classes of specified attribute or variable produces a frequency distribution1, often called a distribution1 for short. The ratio of the number in the individual groups or cells—the cell frequency2 or class frequency2— to the total number is called the relative frequency3 (cf. 133-5) in that group. The term absolute frequency2 is synonymous with class frequency. In demography the term structure4 is often used instead of frequency, and the structure of a population is often studied with respect to a given attribute such as age.
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