SymmetryPlot - Maple Help

Statistics

 SymmetryPlot
 generate symmetry plots

 Calling Sequence SymmetryPlot(X, plotoptions)

Parameters

 X - data sample plotoptions - options to be passed to the plots[display] command

Options

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

Description

 • 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.
 • This function is part of the Statistics package, so it can be used in the short form SymmetryPlot(..) only after executing the command with(Statistics).  However, it can always be accessed through the long form of the command by using Statistics[SymmetryPlot](..).

Examples

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

This data is skewed to the right, and so the points lie above y=x.

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

This data is skewed to the left, and so the points lie below y=x.

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

This data is symmetric, and so the points fall on the line y=x.

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

Added options can customize the plot:

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

The commands to create the plot from the Plotting Guide are

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