compute the average absolute deviation from a given point

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Statistics[AbsoluteDeviation] - compute the average absolute deviation from a given point

	Calling Sequence
	AbsoluteDeviation(A, b, ds_options) AbsoluteDeviation(M, bs, ds_options) AbsoluteDeviation(X, p, rv_options)

Parameters

A	-	Array; data sample
M	-	Matrix; Matrix data set
X	-	algebraic; random variable or distribution
b	-	real number; base point
bs	-	real number or list of real numbers; base points
p	-	algebraic expression; base point
ds_options	-	(optional) equation(s) of the form option=value where option is one of ignore, or weights; specify options for computing the absolute deviation of a data set
rv_options	-	(optional) equation of the form numeric=value; specifies options for computing the absolute deviation of a random variable

Description

•	The AbsoluteDeviation function computes the average absolute deviation of the specified random variable or data set from the specified base point.

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

•

The parameter b must be a real number in the first calling sequence. In the second calling sequence, bs can be a real number or a list of real numbers; a list gives the base points for respective columns of the Matrix data set. If bs is a single real number, then the base point is the same for all columns. In the third calling sequence, p can be any expression of type/algebraic.

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.

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

•	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 AbsoluteDeviation command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the AbsoluteDeviation 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 .

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 absolute deviation is computed symbolically. To compute the absolute deviation numerically, specify the numeric or numeric = true option.

Compatibility

•	The M and bs parameters were introduced in Maple 16.

•	For more information on Maple 16 changes, see Updates in Maple 16.

Examples

Compute the average absolute deviation of the beta distribution with parameters 3 and 5 from point .

(1)

(2)

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

(3)

Compute the standard error of the sample absolute deviation from for the normal distribution with parameters 5 and 2.

[(1/2)*(4*2^(1/2)*exp(-81/32)+9*erf((9/8)*2^(1/2))*Pi^(1/2))/Pi^(1/2), (1/2000)*(97-(4*2^(1/2)*exp(-81/32)+9*erf((9/8)*2^(1/2))*Pi^(1/2))^2/Pi)^(1/2)]

(4)

(5)

(6)

Create a beta-distributed random variable and compute the average absolute deviation of from .

(7)

(8)

Verify this using simulation.

(9)

Compute the average absolute deviation of a weighted data set.

(10)

(11)

Consider the following Matrix data set.

M := Matrix([[3, 1130, 114694], [4, 1527, 127368], [3, 907, 88464], [2, 878, 96484], [4, 995, 128007]])

(12)

We compute the average absolute deviation from a fixed number.

(13)

It might be more useful to take the average absolute deviation from three different numbers.

(14)

	See Also
	Statistics, Statistics[Computation], Statistics[DescriptiveStatistics], Statistics[Distributions], Statistics[ExpectedValue], Statistics[RandomVariables], Statistics[StandardError]