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Statistics

  

StandardDeviation

  

compute the standard deviation

 

Calling Sequence

Parameters

Description

Computation

Data Set Options

Random Variable Options

Examples

References

Compatibility

Calling Sequence

StandardDeviation(A, ds_options)

StandardDeviation(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 standard deviation of a data set

rv_options

-

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

Description

• 

The StandardDeviation function computes the standard deviation of the specified data set or random variable.  In the data set case the unbiased estimate for the variance is used (see Statistics,Variance for more details).

• 

The first parameter can be a 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 StandardDeviation command. Missing items are represented by undefined or Float(undefined). So, if ignore=false and A contains missing data, the StandardDeviation 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 standard deviation is computed using exact arithmetic. To compute the standard deviation numerically, specify the numeric or numeric = true option.

Examples

withStatistics:

Compute the standard deviation of the beta distribution with parameters p and q.

StandardDeviation'Β'p,q

pqp+q+1p+q

(1)

Use numeric parameters.

StandardDeviation'Β'3,5

12415

(2)

StandardDeviation'Β'3,5,numeric

0.1613743061

(3)

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

ASample'Β'3,5,105:

StandardDeviationA

0.162009415371602

(4)

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

XRandomVariableNormal5,2

X_R3

(5)

BSampleX,106:

StandardDeviationX,StandardError[106]StandardDeviation,X

2,110002

(6)

StandardDeviationB

1.99980944723627

(7)

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

YRandomVariable'Β'5,2:

StandardDeviation1Y+2

1213564396708480ln2+16588800ln3ln28294400ln228294400ln32+6708480ln3

(8)

StandardDeviation1Y+2,numeric

0.02274855629

(9)

Verify this using simulation.

CSample1Y+2,105:

StandardDeviationC

0.0227678016319371

(10)

Compute the standard deviation 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:

StandardDeviationV,weights=W

HFloatundefined

(11)

StandardDeviationV,weights=W,ignore=true

2.72742139848191

(12)

Consider the following Matrix data set.

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

M31130114694415271273683907884642878964844995128007

(13)

We compute the standard deviation of each of the columns.

StandardDeviationM

0.836660026534076264.57191838893317953.9731201759

(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 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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