Important: The stats package has been deprecated. Use the superseding package Statistics instead.

The function standardscore of the subpackage stats[transform, ...] replaces each item in data by its standard score.

The standard score of a quantity $x$ is $\frac{x-\mathrm{mean}}{\mathrm{standarddeviation}}$, where mean and $\mathrm{standarddeviation}$ are the mean and the standard deviation  of data, respectively.

Standard scores are also known as zscores, or z-scores.

The quantity n_constraints  is explained in more detail in the description of stats[describe,standarddeviation].

The standard score is very useful in comparing distributions. For example, a student can compare her relative standing between two courses if she knows her mark, the courses averages and standard deviations.

Results expressed in terms of standard score are also known as being expressed in standard units.

By definition, the set of standard scores of a list of statistical data will have mean equal to 0 and standard deviation equal to 1.

Missing items remain unchanged. Weighted data and class data are recognized.

$\mathrm{with}\left(\mathrm{stats}\right)\:$

$\mathrm{data}≔\left[\mathrm{Weight}\left(3\,10\right)\,\mathrm{missing}\,4\,\mathrm{Weight}\left(11..12\,3\right)\right]$

$\mathrm{data}≔\left[\mathrm{Weight}\left(3\,10\right)\,\mathrm{missing}\,4\,\mathrm{Weight}\left(11..12\,3\right)\right]$

$\mathrm{transform}\left[\mathrm{standardscore}\right]\left(\mathrm{data}\right)\:$$\mathrm{transform}\left[\mathrm{apply}\left[\mathrm{evalf}\right]\right]\left(\right)$

$\left[\mathrm{Weight}\left(3.\,10\right)\,\mathrm{missing}\,4.\,\mathrm{Weight}\left(11...12.\,3\right)\right]$

$\mathrm{transform}\left[\mathrm{divideby}\left[\mathrm{standarddeviation}\right]\right]\left(\mathrm{transform}\left[\mathrm{subtractfrom}\left[\mathrm{mean}\right]\right]\left(\mathrm{data}\right)\right)$

$\left[\mathrm{Weight}\left(-\frac{53\sqrt{9385}}{9385}\,10\right)\,\mathrm{missing}\,-\frac{5\sqrt{9385}}{1877}\,\mathrm{Weight}\left(\frac{171\sqrt{9385}}{9385}..\frac{199\sqrt{9385}}{9385}\,3\right)\right]$

$\mathrm{transform}\left[\mathrm{apply}\left[\mathrm{evalf}\right]\right]\left(\right)$

$\left[\mathrm{Weight}\left(\mathrm{-0.5470899427}\,10\right)\,\mathrm{missing}\,\mathrm{-0.2580612937}\,\mathrm{Weight}\left(1.765139249..2.054167898\,3\right)\right]$

$\mathrm{the\_sd}≔\mathrm{describe}\left[\mathrm{standarddeviation}\right]\left(\mathrm{data}\right)$

$\mathrm{the\_sd}≔\frac{\sqrt{9385}}{28}$

$\mathrm{the\_mean}≔\mathrm{describe}\left[\mathrm{mean}\right]\left(\mathrm{data}\right)$

$\mathrm{the\_mean}≔\frac{137}{28}$

$\mathrm{transform}\left[\mathrm{apply}\left[\mathrm{unapply}\left(\frac{x-\mathrm{the\_mean}}{\mathrm{the\_sd}}\,x\right)\right]\right]\left(\mathrm{data}\right)$

$\left[\mathrm{Weight}\left(-\frac{53\sqrt{9385}}{9385}\,10\right)\,\mathrm{missing}\,-\frac{5\sqrt{9385}}{1877}\,\mathrm{Weight}\left(\frac{171\sqrt{9385}}{9385}..\frac{199\sqrt{9385}}{9385}\,3\right)\right]$

$\mathrm{transform}\left[\mathrm{apply}\left[\mathrm{evalf}\right]\right]\left(\right)$

$\left[\mathrm{Weight}\left(\mathrm{-0.5470899427}\,10\right)\,\mathrm{missing}\,\mathrm{-0.2580612937}\,\mathrm{Weight}\left(1.765139249..2.054167898\,3\right)\right]$