Numbers with Uncertainty

The Wolfram Language has built-in capabilities for handling numbers and quantities with uncertainty, as obtained, for example, from measurements.

Around number or quantity x±dx with symmetric or asymmetric uncertainty

VectorAround vector of correlated numbers or quantities with uncertainty

Quantity quantity with units, whose magnitude can include uncertainty

Generating Objects with Uncertainty

MeanAround get the mean of a list of numbers together with its uncertainty

NormalDistribution, ... use a distribution to specify numbers with uncertainty

Interval use an interval to specify numbers with uncertainty

ComputeUncertainty option to generate uncertainty in statistical computations

Uncertainty Propagation

AroundReplace replace variables by uncertain objects, accounting for correlations


ListPlot plot lists with uncertainty indicated by error bars, etc.

ListLinePlot  ▪  ListLogPlot  ▪  DateListPlot  ▪  BarChart  ▪  ...

IntervalMarkers option to specify how error bars' intervals should be plotted

IntervalMarkersStyle coloring, thickness, etc. of error bars

Exact Handling of Distributions

Mean  ▪  StandardDeviation  ▪  Covariance  ▪  TransformedDistribution  ▪  ...