compute the five-point summary for a data sample - Maple Help

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Statistics[FivePointSummary] - compute the five-point summary for a data sample

 Calling Sequence FivePointSummary(data, options)

Parameters

 data - options - (optional) equation(s) of the form option=value where option is one of ignore, output or weights; specify options for the FivePointSummary function

Description

 • The FivePointSummary command computes the minimum, lower hinge, median, upper hinge and the maximum of a data sample. By default, the FivePointSummary command returns a column vector of equations of the form quantity=value where quantity is one of minimum, lowerhinge, median, upperhinge, or maximum.
 • The first parameter A is a data set (e.g., a Vector) or a Matrix data set.

Computation

 • All computations involving data are performed in floating-point; therefore, all data provided must have type realcons and all returned solutions are floating-point, even if the problem is specified with exact values.

Options

 The options argument can contain one or more of the options shown below. Some of these options are described in more detail in the Statistics[DescriptiveStatistics] help page.
 • ignore=truefalse -- This option controls how missing data is handled by the FivePointSummary command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, most of the statistics command will yield undefined. If ignore=true all missing items in A will be ignored. The default value is false.
 • output=default or quantity where quantity is any of minimum, lowerhinge, median, upperhinge, or maximum, indicates which quantities need be calculated. The value of this option can also be a list. In this case the FivePointSummary command will return a list of the specified quantities in the specified order.
 • weights=Vector -- Data weights. The number of elements in the weights array must be equal to the number of elements in the original data sample. By default all elements in A are assigned weight $1$.

Examples

 > $\mathrm{with}\left(\mathrm{Statistics}\right):$
 > $X:=\mathrm{RandomVariable}\left(\mathrm{Normal}\left(10,3\right)\right):$
 > $A:=\mathrm{Sample}\left(X,{10}^{4}\right):$
 > $\mathrm{FivePointSummary}\left(A\right)$
 $\left[\begin{array}{c}{\mathrm{minimum}}{=}{-}{1.61166425663017}\\ {\mathrm{lowerhinge}}{=}{7.91510830185606}\\ {\mathrm{median}}{=}{9.94306123337073}\\ {\mathrm{upperhinge}}{=}{11.9165768932441}\\ {\mathrm{maximum}}{=}{20.7830118018693}\end{array}\right]$ (1)
 > $\mathrm{FivePointSummary}\left(A,\mathrm{output}=\left[\mathrm{lowerhinge},\mathrm{upperhinge}\right]\right)$
 $\left[{7.91510830185606}{,}{11.9165768932441}\right]$ (2)

Note the difference between the quantities computed by the FivePointSummary and the Quantile commands.

 > $\mathrm{FivePointSummary}\left(A,\mathrm{output}=\left[\mathrm{lowerhinge},\mathrm{median},\mathrm{upperhinge}\right]\right)$
 $\left[{7.91510830185606}{,}{9.94306123337073}{,}{11.9165768932441}\right]$ (3)
 > $\mathrm{Quantile}\left(A,\left[0.25,0.5,0.75\right]\right)$
 $\left[{7.91509444943781}{,}{9.94306123337073}{,}{11.9168353743767}\right]$ (4)

Consider the following Matrix data set.

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

We compute the five point summary of each of the columns.

 > $\mathrm{FivePointSummary}\left(M\right)$
 $\left[\begin{array}{ccc}\left[\begin{array}{c}{\mathrm{minimum}}{=}{2.}\\ {\mathrm{lowerhinge}}{=}{3.}\\ {\mathrm{median}}{=}{3.}\\ {\mathrm{upperhinge}}{=}{4.}\\ {\mathrm{maximum}}{=}{4.}\end{array}\right]& \left[\begin{array}{c}{\mathrm{minimum}}{=}{878.}\\ {\mathrm{lowerhinge}}{=}{907.}\\ {\mathrm{median}}{=}{995.}\\ {\mathrm{upperhinge}}{=}{1130.}\\ {\mathrm{maximum}}{=}{1527.}\end{array}\right]& \left[\begin{array}{c}{\mathrm{minimum}}{=}{88464.}\\ {\mathrm{lowerhinge}}{=}{96484.}\\ {\mathrm{median}}{=}{1.14694}{}{{10}}^{{5}}\\ {\mathrm{upperhinge}}{=}{1.27368}{}{{10}}^{{5}}\\ {\mathrm{maximum}}{=}{1.28007}{}{{10}}^{{5}}\end{array}\right]\end{array}\right]$ (6)