standardavvikene

The standard deviation, in statistics, measures the amount of variation or dispersion of a set of values. The term standardavvikene is the plural form in Norwegian. It provides a summary of how spread out the data are around the mean.

The population standard deviation sigma is defined as sqrt( (1/N) sum (x_i - mu)^2 ). The sample standard deviation s is defined as sqrt( (1/(n-1)) sum (x_i - x̄)^2 ). The factor n-1, known as Bessel's correction, makes the estimator of the variance unbiased for samples drawn from a population.

The standard deviation has the same units as the data, is always nonnegative, and is zero only when all observations are identical. It is somewhat sensitive to outliers; extreme values can substantially increase the standard deviation, more so than some other measures of spread.

In a normal distribution, about 68% of observations lie within one standard deviation of the mean, about 95% within two, and about 99.7% within three. This empirical rule provides a sense of how data are distributed around the mean.

Common uses include assessing variability within a population, comparing the variability between datasets, and in finance for measuring risk. Related concepts include variance (the square of the standard deviation) and the standard error of the mean, which estimates the precision of a sample mean.