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in statistics, an important property of a sample. It consists in the closeness of characteristics of the sample—such as composition and average values—to the corresponding characteristics of the population from which the sample has been taken in accordance with established rules (seeSAMPLE SURVEY).
A judgment as to the degree of representativeness of a sample can be made in two ways. First, the sample is compared with the population with respect to all the characteristics that have been measured in both. Thus, in order to judge the representativeness of the sample households selected for a survey of household budgets, the distribution of households with respect to workers’ wage levels can be compared with the analogous distribution derived from general statistical data. If general data on the distribution are not available, average wage levels can be compared.
Second, a judgment as to the degree of representativeness can be made on the basis of the variability of the statistics under investigation in the sample. For example, if the data of a survey of household budgets indicate that the per capita consumption of bread varies from household to household much less than does the consumption of meat, then the sample can be considered to be more representative with respect to the consumption of bread than it is with respect to the consumption of meat.
The representativeness of a sample is measured by the sampling error, which is the difference between a sampling statistic and the parameter of the population from which the sample was taken. In practice, however, this difference remains unknown. Consequently, there is used as a measure of representativeness the probable value of the difference, as determined by the methods of mathematical statistics, or the root mean square of its possible values (see alsoSAMPLING).
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