The Demopædia Encyclopedia on Population is under heavy modernization and maintenance. Outputs could look bizarre, sorry for the temporary inconvenience
14
Disclaimer : The sponsors of Demopaedia do not necessarily agree with all the definitions contained in this version of the Dictionary. Please consult the discussion area of this page for further comments. 

14
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.
* * *
