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Unbiased estimation of standard deviation
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<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a> and in particular <a href="/facts/Statistical_theory/7s5ye1mp">statistical theory</a>, unbiased estimation of a standard deviation is the calculation from a <a href="/facts/Statistical_sample/URCwKNge">statistical sample</a> of an estimated value of the <a href="/facts/Standard_deviation/qSug9BRl">standard deviation</a> (a measure of <a href="/facts/Statistical_dispersion/xqevRHmz">statistical dispersion</a>) of a <a href="/facts/Statistical_population/KAILs8E3">population</a> of values, in such a way that the <a href="/facts/Expected_value/1XV0JKL8">expected value</a> of the calculation equals the true value. Except in some important situations, outlined later, the task has little relevance to applications of statistics since its need is avoided by standard procedures, such as the use of <a href="/facts/Significance_test/yv9RPF6U">significance tests</a> and <a href="/facts/Confidence_intervals/NS8mG5UE">confidence intervals</a>, or by using <a href="/facts/Bayesian_analysis/tEpK3zLx">Bayesian analysis</a>. </p><p>However, for statistical theory, it provides an exemplar problem in the context of <a href="/facts/Estimation_theory/4nbgFDec">estimation theory</a> which is both simple to state and for which results cannot be obtained in closed form. It also provides an example where imposing the requirement for <a href="/facts/Bias_of_an_estimator/oxIvEgmd">unbiased estimation</a> might be seen as just adding inconvenience, with no real benefit. </p>