Descriptive Statistics, Data Summary and Related Commands - Maple Help

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Descriptive Statistics, Data Summary and Related Commands

  

The Statistics package provides various commands for computing descriptive statistics and related quantities. These include location, dispersion and shape statistics, moments and cumulants. The package also provides several data summary and tabulation commands. In addition, most of these functions can handle weighted data and data with missing values. Here is the list of available commands

 

Available Commands

Floating Point Environment

Data with Missing Values

Adding Weights to Data

Examples

Available Commands

Location Statistics

Decile

deciles

GeometricMean

geometric mean

HarmonicMean

harmonic mean

HodgesLehmann

Hodges-Lehmann statistic

MakeProcedure

generate a procedure for calculating statistical quantities

Mean

arithmetic mean

Median

median

Mode

mode

Percentile

percentiles

QuadraticMean

quadratic mean

Quantile

quantiles

Quartile

quartiles

TrimmedMean

trimmed mean

WinsorizedMean

winsorized mean

Dispersion Statistics

AbsoluteDeviation

compute the average absolute deviation

InterquartileRange

interquartile range

MeanDeviation

average absolute deviation from the mean

MedianDeviation

compute the median absolute deviation

Range

range

RousseeuwCrouxQn

Rousseeuw and Croux' Qn

RousseeuwCrouxSn

Rousseeuw and Croux' Sn

StandardDeviation

standard deviation

Variance

variance

Variation

coefficient of variation

Shape Statistics

Kurtosis

kurtosis

Skewness

skewness

Moments and Cumulants

CentralMoment

central moments

Cumulant

cumulants

Moment

moments

StandardizedMoment

standardized moments

Data Summary

DataSummary

seven summary statistics

FivePointSummary

five-point summary

FrequencyTable

frequency table

Related Commands

AutoCorrelation

autocorrelations

Correlation

correlation/correlation matrix

Covariance

covariance/covariance matrix

CrossCorrelation

cross-correlations

ExpectedValue

compute expected values

OrderStatistic

order statistics

PCA

principal component analysis

PrincipalComponentAnalysis

principal component analysis

StandardError

standard error of the sampling distribution

Floating Point Environment

  

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.

Data with Missing Values

  

Missing values are represented by undefined or Float(undefined). Note that Float(undefined) propagates freely through most floating-point operations, which means that most statistics for a data set with missing values will yield undefined. The option ignore - which is available for most commands listed above - controls how missing data is handled. If ignore=true all missing items in a data set will be ignored. The default value of this option is false. For more details on a particular command, see the corresponding help page.

Adding Weights to Data

  

Weights can be added to data by supplying an optional argument weights=value, where value is a vector of numeric constants. The number of elements in the weights array must be equal to the number of elements in the original data set. By default all elements in a data set are assigned weight 1. For more details on a particular command, see the corresponding help page.

Examples

Generate random sample drawn from the non-central Beta distribution.

withStatistics:

XRandomVariableNonCentralBeta3,10,2:

ASampleX,106:

Compute the five point summary of the data sample.

FivePointSummaryA

minimum=0.00284705659174078lowerhinge=0.188161202689945median=0.271067705972343upperhinge=0.364718410290619maximum=0.881224090305735

(1)

Compute the mean, standard deviation, skewness, kurtosis, etc.

DataSummaryA

mean=0.282155087071985standarddeviation=0.125196186114285skewness=0.440928241161531kurtosis=2.84630585844533minimum=0.00284705659174078maximum=0.881224090305735cumulativeweight=1.000000106

(2)

Estimate the mode.

ModeA

0.276805857799331

(3)

Compute the second moment about .3.

MomentA,2,origin=0.3

0.0159925102608858

(4)

Compute mean, trimmed mean and winsorized mean.

MeanA,TrimmedMeanA,1,99,WinsorizedMeanA,1,99

0.282155087072001,0.280925669045912,0.281857130439082

(5)

Compute frequency table for A.

FrequencyTableA,range=0..1,bins=5

0...0.2000000000000002.8399110528.399100002.8399110528.399100000.200000000000000..0.4000000000000005.3668910553.668900008.2068010582.068000000.400000000000000..0.6000000000000001.6888310516.888300009.8956310598.956300000.600000000000000..0.80000000000000010407.1.0407000009.9997010599.997000000.800000000000000..1.30.0.0030000000001.000000106100.0000000

(6)

See Also

Statistics

Statistics[Computation]

Statistics[Distributions]

 


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