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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 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.