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

Statistical (AKA Average Case) Uncertainty

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

ComputeUncertainty — option to generate uncertainty in statistical computations

Uncertainty Propagation

AroundReplace — replace variables by uncertain objects, accounting for correlations

Deterministic (AKA Worst Case) Uncertainty »

Interval — use an interval to specify numbers with uncertainty

CenteredInterval — use a centered interval to specify numbers with uncertainty

Visualization

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  ▪  ...