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

The function scatterplot with the formatting option, format=symmetry of the subpackage stats[statplots] gives a symmetry plot of data.

The data in the data parameter are sorted, and missing items are removed. If the data are indexed by data[i], med is the median of the data  and n is the total number of observations then a plot of ${\mathrm{data}}_{n+1-i}-\mathrm{med}$ versus $\mathrm{med}-{\mathrm{data}}_i$ for all i is produced together with the $y=x$ line.

If the data set is symmetric (with respect to the median), then the plot will produce points on straight line $y=x$. For ease of comparison, the symmetry plot includes this comparison line. Thus, a symmetry plot reveals departures from symmetry.

The actual behavior takes into account the various weight of the data.

Although classes are converted to classmarks when generating this type of plot, it is recommended that only data without classes be used. class data may distort results that can be inferred from the graph.

The command with(stats[statplots] allows the use of the abbreviated form of this command.

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

$\mathrm{data1}≔\left[2.93\,2.58\,2.85\,4.26\,2.94\,4.33\,1.71\,4.42\,3.59\,4.35\,2.07\,1.16\,2.36\,1.16\,4.72\,6\right]\:$

$\mathrm{statplots}\left[\mathrm{scatterplot}\right]\left(\mathrm{data1}\,\mathrm{format}=\mathrm{symmetry}\right)$

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

$\mathrm{plots}\left[\mathrm{display}\right]\left(\mathrm{scatterplot}\left(\mathrm{data1}\,\mathrm{format}=\mathrm{symmetry}\right)\,\mathrm{scaling}=\mathrm{CONSTRAINED}\,\mathrm{view}=\left[0..2.5\,0..2.5\right]\right)$

$\mathrm{data2}≔\left[1\,4\,5\,16\,17\,18\,19\right]$

$\mathrm{data2}≔\left[1\,4\,5\,16\,17\,18\,19\right]$

$\mathrm{scatterplot}\left(\mathrm{data2}\,\mathrm{format}=\mathrm{symmetry}\right)$

$\mathrm{data3}≔\left[1\,3\,4\,5\,6\,7\,9\right]$

$\mathrm{data3}≔\left[1\,3\,4\,5\,6\,7\,9\right]$

$\mathrm{scatterplot}\left(\mathrm{data3}\,\mathrm{format}=\mathrm{symmetry}\right)$