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The plotoptions argument can contain one or more of the options accepted by the plots[display] command. See plot/options for details.

The SymmetryPlot command generates a symmetry plot for the specified data. The elements of X are sorted and plotted in such a way to show which way the data is skewed. If the data is indexed as X[i], med is the median of the data and n is the total number of observations, then a plot of X[n+1-i] - med versus med-X[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 produced will have points lying along the line y=x. Any departure from this symmetry will be visible as points lying off of this line. If the data is skewed to the right, the points will lie above the line. If the data is skewed to the left, the points will lie below the line.

The parameter X is the data to be plotted. It is either a single data sample - given as e.g a Vector - or a list of data samples and does not need to be one dimensional, though it will be treated as though it were. There must be at least two points present for this function to create a plot.

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

$\mathrm{data1}≔\left[1.3\,3.2\,2.1\,4.76\,7.33\,2\,0.91\,5.5\,1\,2.4\right]\:$

$\mathrm{SymmetryPlot}\left(\mathrm{data1}\right)$

$\mathrm{data2}≔\mathrm{Array}\left(\left[\left[1\,4\,5\,13\right]\,\left[15\,12\,14\,16\right]\right]\right)\:$

$\mathrm{SymmetryPlot}\left(\mathrm{data2}\right)$

$\mathrm{data3}≔\mathrm{Vector}\left(\left[1\,2\,3\,4\,5\,6\,7\,8\,9\,10\right]\right)\:$

$\mathrm{SymmetryPlot}\left(\mathrm{data3}\right)$

$\mathrm{SymmetryPlot}\left(\mathrm{data3}\,\mathrm{symbol}=\mathrm{circle}\,\mathrm{symbolsize}=15\,\mathrm{thickness}=2\,\mathrm{axis}=\left[\mathrm{gridlines}=\left[\mathrm{linestyle}=\mathrm{dot}\right]\right]\right)$

$\mathrm{data4}≔\mathrm{Array}\left(\left[\left[1\,4\,5\,13\right]\,\left[15\,12\,14\,16\right]\,\left[6\,2\,14\,13\,12\right]\,\left[2\,9\,16\,12\,10\right]\,\left[3\,8\,2\,10\,14\right]\right]\right)\:$

$\mathrm{SymmetryPlot}\left(\mathrm{data4}\right)$