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The standard deviation of a random variable, sample, statistical population, data set, or probability distribution is the square root of its variance. It is algebraically simpler, though in practice less robust, than the average absolute deviation.
If is a standard normal deviate, then = + will have a normal distribution with expected value and standard deviation . This is equivalent to saying that the standard normal distribution Z {\displaystyle Z} can be scaled/stretched by a factor of σ {\displaystyle \sigma } and shifted by μ {\displaystyle \mu } to yield a different normal ...
Unbiased estimation of standard deviation. In statistics and in particular statistical theory, unbiased estimation of a standard deviation is the calculation from a statistical sample of an estimated value of the standard deviation (a measure of statistical dispersion) of a population of values, in such a way that the expected value of the ...
The second standard deviation from the mean in a normal distribution encompasses a larger portion of the data, covering approximately 95% of the observations. Standard deviation is a widely used measure of the spread or dispersion of a dataset. It quantifies the average amount of variation or deviation of individual data points from the mean of ...
For correlated random variables the sample variance needs to be computed according to the Markov chain central limit theorem.. Independent and identically distributed random variables with random sample size
The unbiased estimation of standard deviation is a technically involved problem, though for the normal distribution using the term n − 1.5 yields an almost unbiased estimator. The unbiased sample variance is a U-statistic for the function ƒ ( y 1 , y 2 ) = ( y 1 − y 2 ) 2 /2, meaning that it is obtained by averaging a 2-sample statistic ...
In other words, for a normal distribution, mean absolute deviation is about 0.8 times the standard deviation. However, in-sample measurements deliver values of the ratio of mean average deviation / standard deviation for a given Gaussian sample n with the following bounds: [,], with a bias for small n.
In probability theory and statistics, the coefficient of variation ( CV ), also known as normalized root-mean-square deviation (NRMSD), percent RMS, and relative standard deviation ( RSD ), is a standardized measure of dispersion of a probability distribution or frequency distribution. It is defined as the ratio of the standard deviation to the ...