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Student[Statistics]

  

StandardDeviation

  

compute the standard deviation

 

Calling Sequence

Parameters

Description

Computation

Examples

References

Compatibility

Calling Sequence

StandardDeviation(A, numeric_option, output_option)

StandardDeviation(M, numeric_option, output_option)

StandardDeviation(X, numeric_option, inert_option, output_option)

Parameters

A

-

data sample

M

-

Matrix data sample

X

-

algebraic; random variable

numeric_option

-

(optional) equation of the form numeric=value where value is true or false

output_option

-

(optional) equation of the form output=x where x is value, plot, or both

inert_option

-

(optional) equation of the form inert=value where value is true or false

Description

• 

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

• 

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

• 

If the option output is not included or is specified to be output=value, then the function will return the value of the standard deviation. If output=plot is specified, then the function will return a plot of the input data set and its standard deviation. If output=both is specified, then both the value and the plot of the standard deviation will be returned.

• 

If the option inert is not included or is specified to be inert=false, then the function will return the actual value of the result. If inert or inert=true is specified, then the function will return the formula of evaluating the actual value.

Computation

• 

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

• 

If there are floating point values or the option numeric is included, then the computation is done in floating point. Otherwise the computation is exact.

• 

By default, the standard deviation is computed according to the rules mentioned above. To always compute the standard deviation numerically, specify the numeric or numeric = true option.

Examples

withStudentStatistics:

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

StandardDeviationBetaRandomVariablep,q

pqp+q+1p+q

(1)

Use the numeric or the output=plot option

StandardDeviationBetaRandomVariable3,5,numeric

0.1613743061

(2)

StandardDeviationBetaRandomVariable3,5,output=plot

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

YBetaRandomVariable5,2:

StandardDeviation1Y+2

13564396708480ln2+16588800ln3ln28294400ln228294400ln32+6708480ln32

(3)

StandardDeviation1Y+2,numeric

0.02274855629

(4)

Compute the standard deviation of a data set, which contains an undefined value

StandardDeviation1,2,4,0,undefined

undefined

(5)

Consider the following Matrix data sample.

MMatrix4,Pi,114694,4.2,15,127368,3.0,7,88464

4π1146944.2151273683.0788464

(6)

Compute the standard deviation of each of the columns.

StandardDeviationM

0.642910050732863812223π2232+223313π2+21313π223885811647

(7)

If the output=both option is included, then both the value and the plot of the standard deviation will be returned.

sd1,graph1StandardDeviationM,output=both:

sd1

0.642910050732863812223π2232+223313π2+21313π223885811647

(8)

graph1

Use both the output=both option and the inert option.

KBinomialRandomVariable5,13:

sd2,graph2StandardDeviationK,output=both,inert:

StandardDeviationK,numeric

1.054092553

(9)

sd2

_t0=05_t0_t=05_t5_t13_t235_t25_t013_t0235_t0

(10)

evalfsd2

1.054092553

(11)

graph2

References

  

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

Compatibility

• 

The Student[Statistics][StandardDeviation] command was introduced in Maple 18.

• 

For more information on Maple 18 changes, see Updates in Maple 18.

See Also

Statistics[StandardDeviation]

Student

Student[Statistics]

Student[Statistics][RandomVariable]