__Statistics:__double**gsl_stats_mean***(const double*`data`[], size_t`stride`, size_t`n`)-
This function returns the arithmetic mean of
`data`, a dataset of length`n`with stride`stride`. The arithmetic mean, or**sample mean**, is denoted by @math{\Hat\mu} and defined as,where @math{x_i} are the elements of the dataset

`data`. For samples drawn from a gaussian distribution the variance of @math{\Hat\mu} is @math{\sigma^2 / N}.

__Statistics:__double**gsl_stats_variance***(const double*`data`[], size_t`stride`, size_t`n`)-
This function returns the estimated, or
**sample**, variance of`data`, a dataset of length`n`with stride`stride`. The estimated variance is denoted by @math{\Hat\sigma^2} and is defined by,where @math{x_i} are the elements of the dataset

`data`. Note that the normalization factor of @math{1/(N-1)} results from the derivation of @math{\Hat\sigma^2} as an unbiased estimator of the population variance @math{\sigma^2}. For samples drawn from a gaussian distribution the variance of @math{\Hat\sigma^2} itself is @math{2 \sigma^4 / N}.This function computes the mean via a call to

`gsl_stats_mean`

. If you have already computed the mean then you can pass it directly to`gsl_stats_variance_m`

.

__Statistics:__double**gsl_stats_variance_m***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`)-
This function returns the sample variance of
`data`relative to the given value of`mean`. The function is computed with @math{\Hat\mu} replaced by the value of`mean`that you supply,

__Statistics:__double**gsl_stats_sd***(const double*`data`[], size_t`stride`, size_t`n`)__Statistics:__double**gsl_stats_sd_m***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`)- The standard deviation is defined as the square root of the variance. These functions return the square root of the corresponding variance functions above.

__Statistics:__double**gsl_stats_variance_with_fixed_mean***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`)-
This function computes an unbiased estimate of the variance of
`data`when the population mean`mean`of the underlying distribution is known*a priori*. In this case the estimator for the variance uses the factor @math{1/N} and the sample mean @math{\Hat\mu} is replaced by the known population mean @math{\mu},

__Statistics:__double**gsl_stats_sd_with_fixed_mean***(const double*`data`[], size_t`stride`, size_t`n`, double`mean`)-
This function calculates the standard deviation of
`data`for a a fixed population mean`mean`. The result is the square root of the corresponding variance function.

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