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Statistics are derived from sample data, and because they are not taken from complete data, they inevitably vary from one sample to another. The standard error is a measure of the expected dispersion of sample estimates around the true population parameter. It is used to gauge the accuracy of a sample estimate: A larger standard error suggests less confidence in the sample statistic as an accurate measure of the population characteristic. Standard errors can be calculated for a range of survey statistics including means, percentages, totals, and differences in percentages. The discussion that follows focuses on sample means and proportions.

In a survey of families, let X represent family income, and let denote the mean family income, which is an example of a statistic resulting ...

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