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Standard deviation
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<p>In <a href="/facts/Statistics/DNPsKGYU">statistics</a>, the standard deviation is a measure of the amount of variation of the values of a variable about its <a href="/facts/Expected_value/1XV0JKL8">mean</a>. A low standard <a href="/facts/Deviation_(statistics)/F7cqnhtF">deviation</a> indicates that the values tend to be close to the <a href="/facts/Mean/swcEd4Pg">mean</a> (also called the <a href="/facts/Expected_value/1XV0JKL8">expected value</a>) of the set, while a high standard deviation indicates that the values are spread out over a wider range. The standard deviation is commonly used in the determination of what constitutes an <a href="/facts/Outlier/VBhIzGbx">outlier</a> and what does not. Standard deviation may be abbreviated SD or std dev, and is most commonly represented in mathematical texts and equations by the lowercase <a href="/facts/Greek_alphabet/1cHwB8Dg">Greek letter</a> <a href="/facts/Sigma/DWcCDzou">σ</a> (sigma), for the population standard deviation, or the <a href="/facts/Latin_script/7EWeJjUV">Latin letter</a> <i><a href="/facts/S/1DcekgEL">s</a></i>, for the sample standard deviation. </p><p>The standard deviation of a <a href="/facts/Random_variable/TwTBXnLT">random variable</a>, <a href="/facts/Sample_(statistics)/URCwKNge">sample</a>, <a href="/facts/Statistical_population/KAILs8E3">statistical population</a>, <a href="/facts/Data_set/eDvegUTK">data set</a>, or <a href="/facts/Probability_distribution/EpsKKVRu">probability distribution</a> is the <a href="/facts/Square_root/AfrzfBdQ">square root</a> of its <a href="/facts/Variance/ULBJKXD1">variance</a>. (For a finite population, variance is the average of the <a href="/facts/Squared_deviations_from_the_mean/qMoU6JGp">squared deviations from the mean</a>.) A useful property of the standard deviation is that, unlike the variance, it is expressed in the same unit as the data. Standard deviation can also be used to calculate <a href="/facts/Standard_error/Iv96AyCD">standard error</a> for a finite sample, and to determine <a href="/facts/Statistical_significance/PMxjdlAu">statistical significance</a>. </p><p>When only a <a href="/facts/Statistical_sample/URCwKNge">sample</a> of data from a population is available, the term <i>standard deviation of the sample</i> or <i>sample standard deviation</i> can refer to either the above-mentioned quantity as applied to those data, or to a modified quantity that is an unbiased estimate of the <i>population standard deviation</i> (the standard deviation of the entire population). </p>