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
Floating Point Environment
Data with Missing Values
Adding Weights to Data
generate a procedure for calculating statistical quantities
compute the average absolute deviation
average absolute deviation from the mean
compute the median absolute deviation
Rousseeuw and Croux' Qn
Rousseeuw and Croux' Sn
coefficient of variation
Moments and Cumulants
seven summary statistics
compute expected values
principal component analysis
standard error of the sampling distribution
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.
Most of the commands above can accept one- and two-dimensional data sets. One-dimensional data sets can be supplied as a list, a Vector, a one-dimensional Array, or a DataSeries. Two-dimensional data sets can be supplied as a list of lists, a Matrix, a two-dimensional Array, or a DataFrame.
For more details on how two-dimensional data is handled, see the DataFrames in Statistics help page.
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.
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.
Generate random sample drawn from the non-central Beta distribution.
X ≔ RandomVariable⁡NonCentralBeta⁡3,10,2:
A ≔ Sample⁡X,106:
Compute the five point summary of the data sample.
Compute the mean, standard deviation, skewness, kurtosis, etc.
Estimate the mode.
Compute the second moment about .3.
Compute mean, trimmed mean and winsorized mean.
Compute frequency table for A.
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