# Absolute Deviation

An Absolute Deviation is an absolute difference between any given element in a dataset and its mean .

## References

### 2016

$\displaystyle{ D_i = |x_i-m(X)| }$
where
Di is the absolute deviation,
xi is the data element
and m(X) is the chosen measure of central tendency of the data set — sometimes the mean ($\displaystyle{ \overline{x} }$), but most often the median.

### 2016

$\displaystyle{ \Delta u_i\equiv|u_i-\bar{u}| }$

### 2016

This function computes the absolute deviation from the mean of data, a dataset of length n with stride stride. The absolute deviation from the mean is defined as,
absdev = (1/N) \sum |x_i - \Hat\mu|
where x_i are the elements of the dataset data. The absolute deviation from the mean provides a more robust measure of the width of a distribution than the variance. This function computes the mean of data via a call to gsl_stats_mean.
Function: double gsl_stats_absdev_m (const double data[], size_t stride, size_t n, double mean)
This function computes the absolute deviation of the dataset data relative to the given value of mean,
absdev = (1/N) \sum |x_i - mean|
This function is useful if you have already computed the mean of data (and want to avoid recomputing it), or wish to calculate the absolute deviation relative to another value (such as zero, or the median).