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Statistics

  

Mean

  

compute the arithmetic mean

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

Mean(A, ds_options)

Mean(M, ds_options)

Mean(X, rv_options)

Parameters

A

-

data sample

M

-

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 mean of a data set

rv_options

-

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

Description

• 

The Mean function computes the arithmetic mean 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]).

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 Mean command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the Mean 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 mean is computed using exact arithmetic. To compute the mean numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the mean of the beta distribution with parameters p and q.

Mean'Β'p,q

pp+q

(1)

Use numeric parameters.

Mean'Β'3,5

38

(2)

Mean'Β'3,5,numeric

0.3750000000

(3)

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

ASample'Β'3,5,105:

MeanA

0.374639034959981

(4)

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

XNormal5,2

X:=Normal5,2

(5)

BSampleX,106:

MeanX,StandardError[106]Mean,X

5,1500

(6)

MeanB

4.99780357414757

(7)

Create a beta-distributed random variable Y and compute the mean of 1Y+2.

YRandomVariable'Β'5,2:

Mean1Y+2

1440ln211672+1440ln3

(8)

Mean1Y+2,numeric

0.3697556758

(9)

Verify this using simulation.

CSample1Y+2,105:

MeanC

0.369740688462993

(10)

Compute the mean 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:

MeanV,weights=W

HFloatundefined

(11)

MeanV,weights=W,ignore=true

67.0208503203261

(12)

Consider the following Matrix data set.

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

M:=31130114694415271273683907884642878964844995128007

(13)

We compute the mean of each of the columns.

MeanM

3.200000000000001087.400000000001.11003400000000105

(14)

References

  

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

Compatibility

• 

The M parameter was introduced in Maple 16.

• 

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

See Also

Statistics

Statistics[Computation]

Statistics[DescriptiveStatistics]

Statistics[Distributions]

Statistics[ExpectedValue]

Statistics[RandomVariables]

Statistics[StandardError]

 


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