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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 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 mean ^{3} or geometric average ^{3} 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 average ^{4} or weighted mean ^{4} is obtained when different items are given varying importance by multiplying each item by a particular 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 most frequent value of a set of observations
 8. mode n. — modal adj.
141
The dispersion ^{1}, scatter ^{1}, variation ^{1} (1503) or variability ^{1} of a set of observations depends on the differences ^{2} or deviations ^{2} (1503) between its elements, Here the most common measures of dispersion ^{3} only are mentioned. The range ^{4} is the difference between the largest and the smallest value of a set of elements. The interquartile range ^{5} is the difference between the first and third quartiles (cf. paragraph 142) and contains half the observations of the set. The semiinterquartile 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 (1402) of the positive values of the deviations of 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 called quantiles ^{1} or order statistics ^{1}. The median (1406) has already been mentioned. Other important order statistics are the quartiles ^{2}, the deciles ^{3} and the percentiles ^{4} or, centiles ^{4}, which divide the population into four, ten and a hundred equal parts respectively.
143
A variable is continuous ^{1} 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 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 specified attribute or variable produces a frequency distribution ^{1}, often called a distribution ^{1} for short. The ratio of the number in the individual groups or cells—the cell frequency ^{2} or class frequency ^{2}— to the total number is called the relative frequency ^{3} (cf. 1335) in that group. The term absolute frequency ^{2} is synonymous with class frequency. In demography the term structure ^{4} 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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