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Student[Statistics]

 DataSummary
 compute six summary statistics for a data sample

 Calling Sequence DataSummary(A, numeric_option, output_option, quantity_option) DataSummary(M, numeric_option, output_option, quantity_option)

Parameters

 A - M - numeric_option - (optional) equation of the form numeric=value where value is true or false output_option - (optional) equation of the form output=x where x is value, plot, or both quantity_option - (optional) equation of the form quantity=y where y is one of mean, standarddeviation, skewness, kurtosis, minimum and maximum, or a list of these names

Description

 • The DataSummary function computes six summary statistics for the input data set. These include the mean, standard deviation, coefficient of skewness, coefficient of kurtosis, minimum and maximum of the sample. By default the DataSummary command returns a list of equations of the form quantity=value where quantity is one of mean, standarddeviation, skewness, kurtosis, minimum, or maximum.
 • The first parameter can be a data sample (e.g., a Vector), or a Matrix data sample.
 • If the option quantity is not included, then data summary is a list of equations defining the mean, standard deviation, coefficient of skewness, coefficient of kurtosis, minimum and maximum. If quantity is one of the names mean, standarddeviation, skewness, kurtosis, minimum, or maximum, then the data summary is just that value. Finally, if quantity is a list of these names, then the data summary is a list of equations defining these quantities.
 • If the option output is not included or is specified to be output=value, then the function will return the value of the data summary. If output=plot is specified, then the function will return a plot of the input data set and all of its statistics. If output=both is specified, then both the value and the plot of the data summary will be returned.

Computation

 • If there are floating point values or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.
 • If the option output is not included or is specified to be output= value, then the function will return the data summary: those statistics specified by the expect option, or all of them if the expect option is not present. If output=plot is specified, then the function will return a plot of the input data set and all selected statistics. If output=both is specified, then both the value and the plot of the data summary will be returned.

Examples

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

Compute the data summary of the following data sample.

 > $A≔⟨-4,\mathrm{Pi},{ⅇ}^{3}⟩$
 $\left[\begin{array}{c}-4\\ \mathrm{π}\\ {ⅇ}^{3}\end{array}\right]$ (1)
 > $\mathrm{DataSummary}\left(A,\mathrm{quantity}=\mathrm{mean}\right)$
 ${-}\frac{{4}}{{3}}{+}\frac{{\mathrm{\pi }}}{{3}}{+}\frac{{{ⅇ}}^{{3}}}{{3}}$ (2)

Use numeric option.

 > $\mathrm{DataSummary}\left(A,\mathrm{numeric}\right)$
 $\left[{\mathrm{mean}}{=}{6.40904319225915}{,}{\mathrm{standarddeviation}}{=}{12.3707496533778}{,}{\mathrm{skewness}}{=}{0.368551181161869}{,}{\mathrm{kurtosis}}{=}{0.999999999227709}{,}{\mathrm{minimum}}{=}{-4.}{,}{\mathrm{maximum}}{=}{20.08553692}\right]$ (3)

If you specify quantity=[mean,maximum], then only the mean and the maximum will be returned.

 > $\mathrm{DataSummary}\left(A,\mathrm{quantity}=\left[\mathrm{mean},\mathrm{maximum}\right]\right)$
 $\left[{-}\frac{{4}}{{3}}{+}\frac{{\mathrm{\pi }}}{{3}}{+}\frac{{{ⅇ}}^{{3}}}{{3}}{,}{{ⅇ}}^{{3}}\right]$ (4)

If output=plot is specified, then a plot will be returned.

 > $\mathrm{DataSummary}\left(A,\mathrm{output}=\mathrm{plot}\right)$ Consider the following Matrix data sample.

 > $M≔\mathrm{Matrix}\left(\left[\left[3,1130,114694\right],\left[4,1527,127368\right],\left[3,907,88464\right],\left[2,878,96484\right],\left[4,995,128007\right]\right]\right)$
 $\left[\begin{array}{rrr}3& 1130& 114694\\ 4& 1527& 127368\\ 3& 907& 88464\\ 2& 878& 96484\\ 4& 995& 128007\end{array}\right]$ (5)

Compute the data summary of each of the columns.

 > $\mathrm{DataSummary}\left(M,\mathrm{numeric}\right)$
 $\left[\begin{array}{ccc}\left[\mathrm{mean}=3.2,\mathrm{standarddeviation}=0.8366600265340756,\mathrm{skewness}=-0.3073444995431305,\mathrm{kurtosis}=1.4775510204081637,\mathrm{minimum}=2.,\mathrm{maximum}=4.\right]& \left[\mathrm{mean}=1087.4,\mathrm{standarddeviation}=264.57191838893254,\mathrm{skewness}=0.9339774575409037,\mathrm{kurtosis}=2.0614694674978806,\mathrm{minimum}=878.,\mathrm{maximum}=1527.\right]& \left[\mathrm{mean}=1.110034{10}^{5},\mathrm{standarddeviation}=17953.973120175935,\mathrm{skewness}=-0.22301188518436266,\mathrm{kurtosis}=1.1020141039120812,\mathrm{minimum}=88464.,\mathrm{maximum}=1.28007{10}^{5}\right]\end{array}\right]$ (6)

Specify the output=both option to obtain both the value and plot of the data summary.

 > $\mathrm{datasummary},\mathrm{graph}≔\mathrm{DataSummary}\left(M,\mathrm{numeric},\mathrm{output}=\mathrm{both}\right)$
 ${\mathrm{datasummary}}{,}{\mathrm{graph}}{≔}\left[\begin{array}{ccc}\left[{\mathrm{mean}}{=}{3.20000000000000}{,}{\mathrm{standarddeviation}}{=}{0.836660026534076}{,}{\mathrm{skewness}}{=}{-0.307344499543130}{,}{\mathrm{kurtosis}}{=}{1.47755102040816}{,}{\mathrm{minimum}}{=}{2.}{,}{\mathrm{maximum}}{=}{4.}\right]& \left[{\mathrm{mean}}{=}{1087.40000000000}{,}{\mathrm{standarddeviation}}{=}{264.571918388933}{,}{\mathrm{skewness}}{=}{0.933977457540904}{,}{\mathrm{kurtosis}}{=}{2.06146946749788}{,}{\mathrm{minimum}}{=}{878.}{,}{\mathrm{maximum}}{=}{1527.}\right]& \left[{\mathrm{mean}}{=}{111003.400000000}{,}{\mathrm{standarddeviation}}{=}{17953.9731201759}{,}{\mathrm{skewness}}{=}{-0.223011885184363}{,}{\mathrm{kurtosis}}{=}{1.10201410391208}{,}{\mathrm{minimum}}{=}{88464.}{,}{\mathrm{maximum}}{=}{128007.}\right]\end{array}\right]{,}{}$ (7)
 > $\mathrm{datasummary}$
 $\left[\begin{array}{ccc}\left[\mathrm{mean}=3.2,\mathrm{standarddeviation}=0.8366600265340756,\mathrm{skewness}=-0.3073444995431305,\mathrm{kurtosis}=1.4775510204081637,\mathrm{minimum}=2.,\mathrm{maximum}=4.\right]& \left[\mathrm{mean}=1087.4,\mathrm{standarddeviation}=264.57191838893254,\mathrm{skewness}=0.9339774575409037,\mathrm{kurtosis}=2.0614694674978806,\mathrm{minimum}=878.,\mathrm{maximum}=1527.\right]& \left[\mathrm{mean}=1.110034{10}^{5},\mathrm{standarddeviation}=17953.973120175935,\mathrm{skewness}=-0.22301188518436266,\mathrm{kurtosis}=1.1020141039120812,\mathrm{minimum}=88464.,\mathrm{maximum}=1.28007{10}^{5}\right]\end{array}\right]$ (8)
 > $\mathrm{graph}$   > 

References

 Stuart, Alan, and Ord, Keith. Kendall's Advanced Theory of Statistics. 6th ed. London: Edward Arnold, 1998. Vol. 1: Distribution Theory.

Compatibility

 • The Student[Statistics][DataSummary] command was introduced in Maple 18.
 • For more information on Maple 18 changes, see Updates in Maple 18.