Standard Deviation

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(x_i − 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 x_i and the mean, divided by n, is calculated and these values are added together.