In mathematical statistics, why are sufficient statistics useful and what does it mean for a statistic to be sufficient?

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter8: Sequences, Series, And Probability
Section8.7: Probability
Problem 58E: What is meant by the sample space of an experiment?
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In mathematical statistics, why are sufficient statistics useful and what does it mean for a statistic to be sufficient?

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A sufficient statistic is statistics summing up all the information in a sample about a parameter chosen. For instance, the mean sample, x̄, estimate the mean population, μ. x̄ is a good statistical value if it preserves all the population mean information found in the original data points.

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