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Statistics

  

Median

  

compute the median

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

Median(A, ds_options)

Median(X, rv_options)

Parameters

A

-

data set or Matrix data set

X

-

algebraic; random variable or distribution

ds_options

-

(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the median of a data set

rv_options

-

(optional) equation of the form numeric=value; specifies options for computing the median of a random variable

Description

• 

The Median function computes the median of the specified random variable or data set.

• 

The first parameter can be a data set (e.g., a Vector), a Matrix data set, a distribution (see Statistics[Distribution]), a random variable, or an algebraic expression involving random variables (see Statistics[RandomVariable]).

• 

In the first calling sequence, if A has an even number of data points, then the median is the mean of the two middle data points.

• 

In the second calling sequence, if X is a discrete random variable, then the median is defined as the first point t such that the CDF at t is greater than or equal to 12.

Computation

• 

By default, all computations involving random variables are performed symbolically (see option numeric below).

• 

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.

Data Set Options

  

The ds_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[DescriptiveStatistics] help page.

• 

ignore=truefalse -- This option controls how missing data is handled by the Median command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Median command will return undefined. If ignore=true all missing items in A will be ignored. The default value is false.

• 

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.

Random Variable Options

  

The rv_options argument can contain one or more of the options shown below. More information for some options is available in the Statistics[RandomVariables] help page.

• 

numeric=truefalse -- By default, the median is computed using exact arithmetic. To compute the median numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the median of the Weibull distribution with parameters p and q.

MedianWeibullp,q

pln21q

(1)

Use numeric parameters.

MedianWeibull3,5

3ln21/5

(2)

MedianWeibull3,5,numeric

2.787958770

(3)

Generate a random sample of size 100000 drawn from the above distribution and compute the sample median.

ASampleWeibull3,5,105:

MedianA

2.78854409375312

(4)

Compute the standard error of the sample median for the normal distribution with parameters 5 and 2.

XNormal5,2

X:=Normal5,2

(5)

BSampleX,106:

MedianX,numeric,StandardError[106]Median,X,numeric

5.,0.00250662827550447

(6)

MedianB

4.99658802235597

(7)

Compute the median of a sum of two random variables.

XRandomVariableNormal5,2:

YRandomVariableNormal10,1:

MedianX+Y

15

(8)

Verify this using simulation.

CSampleX+Y,105:

MedianC

15.0133882319504

(9)

Compute the median of a weighted data set.

Vseqi,i=57..77,undefined:

W2,4,14,41,83,169,394,669,990,1223,1329,1230,1063,646,392,202,79,32,16,5,2,5:

MedianV,weights=W

67.

(10)

MedianV,weights=W,ignore=true

67.

(11)

Consider the following Matrix data set.

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

M:=31130114694415271273683907884642878964844995128007

(12)

We compute the median of each of the columns.

MedianM

3.995.1.14694105

(13)

References

  

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

Compatibility

• 

The A parameter was updated in Maple 16.

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

Statistics[Distributions]

Statistics[ExpectedValue]

Statistics[RandomVariables]

Statistics[StandardError]

 


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