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# 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 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 (150-3) or variability 1 of a set of observations depends on the differences 2 or deviations 2 (150-3) 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 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 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 (140-6) 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. 133-5) 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.