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130
The terms population statistics ^{1} or demographic statistics ^{1} (1022), when used in the singular, denote methods of quantitative analysis of population data, or, more generally, the art of collecting and presenting statistical information about the population. When used in the plural (cf. 102,2) they refer to numerical data ^{2} about populations, which are based on observations ^{3}. After such observations have been collected ^{4}, edited ^{5} or scrutinized ^{5} to eliminate obvious inconsistencies, they are tabulated ^{6} by grouping ^{7} or classifying ^{7} (cf. 2215) them into different groups ^{8} or classes ^{9} (cf. 1162*). The processes from editing to tabulation are sometimes referred to as the collation ^{9} of data.
 1. statistics n. — statistical adj. — statistician n., a specialist in statistics.
 4. collect v. — collection n,
 5. edit v. — editing n. scrutinize v. — scrutiny n.
 6. tabulate v. — tabulation n.
 7. classify v. — classification n. 9. collation n. — collate v.
131
The basic data ^{1}, raw data ^{1}, primary data ^{1}, or crude data ^{1} consist of a series ^{2} of numbers ^{3} or figures ^{3} (cf. 1552) which are put together in the form of a statistical table ^{4}. In such a table the data are generally classified with respect to certain variables ^{5} or variates ^{5} such as age, number of children, etc., or with respect to certain qualities ^{6}, characteristics ^{6} or attributes ^{6} such as sex. Where data are classified with respect to several variables or attributes simultaneously the tables are called crosstabulations ^{7}. Summary tables ^{8} give information in rather less detail than do individual tables ^{9}.
132
For purposes of analysis ^{1} it is usually necessary to obtain more refined figures ^{2} from the raw data (1311). The first stage in the analysis of data frequently consists of the computation ^{3} of ratios, proportions, percentages, or rates (cf. paragraph 133). The last three are particular types of ratio.
 1. analysis n. — analytical adj. — analyse v.
 3. computation n. — compute v, — computer or computer n., one who is engaged in computation. The term "computer" has recently also been used for computing machines.
133
A ratio ^{1} is a quotient which indicates the relation in size of one number to another. A proportion ^{2} is a ratio which indicates the relation in magnitude of a part to the whole. A percentage ^{3} is a proportion in a hundred. A rate ^{4} was initially a special type of ratio used to indicate the relative frequency ^{5} (cf. 1443) of the occurrence of a particular event within a population or subpopulation. The term has, however, acquired a steadily wider meaning and is often used as a synonym for ratio. It is nowadays used in many different senses but the concept of ratio is common to them all.
 2. proportion n. — proportional adj.
 4. Rates are generally given per thousand, and where the term "rate" is used without qualification this is understood. Some rates, however, are given per ten thousand, per hundred thousand or per million, e.g. cause mortality rates (cf. 4217). On other occasions rates may be given per head or per person. The word "rate" is sometimes omitted, thus one may find the expression "a mortality of ten per thousand", but this is not recommended.
134
The relative frequency (1335) of an event is often regarded as the probability ^{1} of occurrence of that event. If this is done, all the individuals who appear in the denominator must have been exposed to risk ^{3} in some way, i. e., there must have been a chance ^{2} or risk ^{2} that the event in question could happen to them. The use of the term "risk" or "chance" does not imply that the event in question is in any way unwanted — thus the term "risk of marriage" is used. The population is often divided into different subgroups, in which the risk of the event in question is less variable between individuals than in the population as a whole; the subgroup is more homogeneous ^{4} with respect to the risk than the relatively heterogeneous ^{5} whole population. Rates calculated for such subgroups are called specific rates ^{6}, as opposed to general rates ^{7} or crude rates (1358) which apply to the population as a whole.
 1. probability n. — probable adj.
 4. homogeneous adj. — homogeneity n.
 5. heterogeneous adj. — heterogeneity n.
135
Data are called provisional ^{1} if they are based on incomplete or insufficiently controlled observations. They are replaced by final ^{2} data when the observations are complete. Rates based on such data are called provisional rates ^{3} and final rates ^{4} respectively. Where unexpected information becomes available after figures have already been published, revised rates ^{5} may be issued. The expression corrected rate ^{6} usually implies that defective data or inappropriate methods have yielded results which are either misleading or of limited value for the purpose in hand and that an effort has been made to correct this, e. g. correction for underenumeration, correction for migration, correction for seasonal movement. Standardized rates ^{7} or adjusted rates ^{7} are designed to make it possible to compare different populations with respect to a variable, e. g. fertility or mortality, where the influence of another variable e. g. age, is held constant. The term corrected rate ^{7} has been used by some demographers as a synonym for standardized rate. Unstandardized rates are called crude rates ^{8}. Although they may be used to measure actual trends, false inferences may result from their uncritical use when populations with different structures (1444) are compared.
(It should be emphasized that there is no uniformly accepted terminology for the subjects mentioned in this paragraph and that the terms are often used rather loosely.)
136
In its most general sense, the term index ^{1} (pl. indexes or indices) or the term indicator ^{1}, is employed for any number measuring a given quantity; but in a more restricted sense an index ^{2} is a ratio showing the value of a given quantity relatively to a base ^{3}, which is conventionally taken as 100.
137
Demographic indices (136. 1) will in most cases relate to a particular period of observation ^{1}; this is true in particular of most rates (1334). An annual rate ^{2} will relate to a period of twelve months. Where observations are collected for a number of years and then averaged, the term mean annual rate ^{3} is often used for the result. Where rates are calculated for periods different from a year they are often converted to an annual basis ^{4} through multiplication by an appropriate factor. Instantaneous rates ^{5} are sometimes computed; they relate to an infinitesimal period of time, cf. for instance the instantaneous death rate (4324) or the instantaneous rate of population growth (7011).
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