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

-

data set or Matrix data set

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.

• 

For more information about computation in the Statistics package, see the Statistics[Computation] help page.

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

withStatistics:

X:=RandomVariableNormal10,3:

A:=SampleX,104:

FivePointSummaryA

minimum=1.61166425663017lowerhinge=7.91510830185606median=9.94306123337073upperhinge=11.9165768932441maximum=20.7830118018693

(1)

FivePointSummaryA,output=lowerhinge,upperhinge

7.91510830185606,11.9165768932441

(2)

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

FivePointSummaryA,output=lowerhinge,median,upperhinge

7.91510830185606,9.94306123337073,11.9165768932441

(3)

QuantileA,0.25,0.5,0.75

7.91509444943781,9.94306123337073,11.9168353743767

(4)

Consider the following Matrix data set.

M:=Matrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M:=31130114694415271273683907884642878964844995128007

(5)

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

FivePointSummaryM

minimum=2.lowerhinge=3.median=3.upperhinge=4.maximum=4.minimum=878.lowerhinge=907.median=995.upperhinge=1130.maximum=1527.minimum=88464.lowerhinge=96484.median=1.14694105upperhinge=1.27368105maximum=1.28007105

(6)

See Also

Statistics, Statistics[Computation], Statistics[DescriptiveStatistics]

References

  

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


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