When researchers ask for a nationally representative ("nat. rep.") sample, they mean that the population of interest is the entire population of the country in question and that the sample should reflect this in its structure. At its best then the nat. rep. sample will 'look like' the population irrespective of how it is viewed. The numbers of men vs. women will match the national proportions, the percentage in each age group or each region will exactly match the population etc. On non-demographic measures (such as product ownership or psychographics) the sample should match the population.
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