16 Facts About Standard deviation

In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values.

The mean's standard error turns out to equal the population standard deviation divided by the square root of the sample size, and is estimated by using the sample standard deviation divided by the square root of the sample size.

The normal distribution has tails going out to infinity, but its mean and standard deviation do exist, because the tails diminish quickly enough.

In cases where that cannot be done, the standard deviation s is estimated by examining a random sample taken from the population and computing a statistic of the sample, which is used as an estimate of the population standard deviation.

Unlike in the case of estimating the population mean, for which the sample mean is a simple estimator with many desirable properties, there is no single estimator for the standard deviation with all these properties, and unbiased estimation of standard deviation is a very technically involved problem.

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Formula for the population standard deviation can be applied to the sample, using the size of the sample as the size of the population .

Standard deviation we obtain by sampling a distribution is itself not absolutely accurate, both for mathematical reasons and for practical reasons of measurement .

Standard deviation is invariant under changes in location, and scales directly with the scale of the random variable.

Which means that the standard deviation is equal to the square root of the difference between the average of the squares of the values and the square of the average value.

Large standard deviation indicates that the data points can spread far from the mean and a small standard deviation indicates that they are clustered closely around the mean.

Standard deviation is often used to compare real-world data against a model to test the model.

Standard deviation provides a quantified estimate of the uncertainty of future returns.

Population standard deviation is used to set the width of Bollinger Bands, a technical analysis tool.

Where µ is the expected value of the random variables, s equals their distribution's standard deviation divided by n, and n is the number of random variables.

The standard deviation therefore is simply a scaling variable that adjusts how broad the curve will be, though it appears in the normalizing constant.

Term standard deviation was first used in writing by Karl Pearson in 1894, following his use of it in lectures.