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standard deviation

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standard deviation, in statistics, a measure of the variability (dispersion or spread) of any set of numerical values about their arithmetic mean (average; denoted by μ). It is specifically defined as the positive square root of the variance (σ2); in symbols, σ2 = Σ(xi − μ)2/n, where Σ is a compact notation used to indicate that as the index (i) changes from 1 to n (the number of elements in the data set), the square of the difference between each element xi and the mean, divided by n, is calculated and these values are added together.