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Statistics

  

FivePointSummary

  

compute the five-point summary for a data sample

 

Calling Sequence

Parameters

Options

Description

Computation

Examples

References

Compatibility

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, summarize, or weights; specify options for the FivePointSummary function

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.

• 

summarize : false or embed; Display an embedded summary table. The default is false.

• 

weights : Vector of 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.

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.

Examples

withStatistics:

XRandomVariableNormal10,3:

ASampleX,104:

The FivePointSummary command returns a Vector containing the summary statistics.

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.

MMatrix3,1130,114694,4,1527,127368,3,907,88464,2,878,96484,4,995,128007

M31130114694415271273683907884642878964844995128007

(5)

For Matrix input, the FivePointSummary command outputs a Vector containing the corresponding summary statistics by column.

resultsFivePointSummaryM

resultsminimum=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)

To display the summary for one of the columns:

results1

minimum=2.lowerhinge=3.median=3.upperhinge=4.maximum=4.

(7)

If the input is a DataFrame object, then the result is a DataFrame that has the same column labels as the original input, and the row labels correspond to the output quantities requested.

dfDataFrameM,columns=a,b,c

dfabc1311301146942415271273683390788464428789648454995128007

(8)

df_resultsFivePointSummarydf

df_resultsabcminimum2.878.88464.lowerhinge3.907.96484.median3.995.1.14694105upperhinge4.1130.1.27368105maximum4.1527.1.28007105

(9)

df_resultsb

minimum878.lowerhinge907.median995.upperhinge1130.maximum1527.

(10)

The summarize option makes it possible to display an embedded table containing the results. Note that the embedded table is only for display and that the returned value of the FivePointSummary command is unchanged.

resultsFivePointSummaryM,summarize=embed:

 

1

2

3

minimum

2.0

878.0

88464.0

lowerhinge

3.0

907.0

96484.0

median

3.0

995.0

1.146940105

upperhinge

4.0

1130.0

1.273680105

maximum

4.0

1527.0

1.280070105

Similar to the previous example, the returned value for results is the same:

results1

minimum=2.lowerhinge=3.median=3.upperhinge=4.maximum=4.

(11)

References

  

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

Compatibility

• 

The data parameter was updated in Maple 16.

• 

The Statistics[FivePointSummary] command was updated in Maple 2016.

• 

The summarize option was introduced in Maple 2016.

• 

For more information on Maple 2016 changes, see Updates in Maple 2016.

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

 


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