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Statistics[SymmetryPlot] - generate symmetry plots

Calling Sequence

SymmetryPlot(X, plotoptions)

Parameters

X

-

data sample

plotoptions

-

options to be passed to the plots[display] command

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 sample to be plotted. It can be given as a Vector, Matrix, Array, or list 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

withStatistics:

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

data1:=1.3,3.2,2.1,4.76,7.33,2,0.91,5.5,1,2.4:

SymmetryPlotdata1

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

data2:=Array1,4,5,13,15,12,14,16:

SymmetryPlotdata2

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

data3:=Vector1,2,3,4,5,6,7,8,9,10:

SymmetryPlotdata3

The commands to create the plot from the Plotting Guide are

data4:=Array1,4,5,13,15,12,14,16,6,2,14,13,12,2,9,16,12,10,3,8,2,10,14:

SymmetryPlotdata4

See Also

plot[options], plots[display], Statistics, Statistics[Visualization]


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