Around

Around[x,δ]

represents an approximate number or quantity with a value around x and an uncertainty δ.

Around[x,{δ-,δ+}]

represents a number or quantity with a value around x and asymmetric uncertainties δ-, δ+.

Around[dist]

gives an approximate number or quantity around the mean of the distribution dist, with an uncertainty corresponding to the standard deviation of the distribution.

Around[s]

gives an approximate object derived from the number, interval or string specification s.

Details

  • Around[x,δ] is typically displayed as x±δ. If δ is very small compared to x, as in Around[1.2345678,0.0000012], it is instead displayed in a form like .
  • Around[x,δ] can be used to represent results of measurements in which there is statistical or other uncertainty.
  • Around[x,Scaled[ϕ]] represents a number with relative error ϕ, corresponding to Around[x,ϕ x].
  • When Around is used in computations, uncertainties are by default propagated using a first-order series approximation, assuming no correlations.
  • Around[]["prop"] can be used to extract the following properties:
  • "Value"central value x in Around[x,δ]
    "Uncertainty"uncertainty δ in Around[x,δ]
    "Number"number with value x and accuracy corresponding to δ
    "Interval"Interval[{x-δ,x+δ}]
  • In Around[s], numbers with uncertainty can be specified as follows:
  • x (approximate number)Around[x,10^-Accuracy[x]]
    Interval[{xmin,xmax}]Around[(xmax+xmin)/2,(xmax-xmin)/2]
    dist (statistical distribution)Around[Mean[dist],StandardDeviation[dist]]
    "nn.dddd" (number string)(uncertainty determined by number of significant digits)
  • For linear computations, Around[x,δ] behaves like a number whose values are distributed according to the normal distribution NormalDistribution[x,δ].
  • In Around[x,δ], the value x and the uncertainty δ can be any numeric or symbolic expressions. If δ is a numeric expression, then both x and δ will be made numerical. By default, machine precision will be used, but higher precision may be used if needed to represent the numbers faithfully.
  • Around[x,δ] displays with one or two digits of the uncertainty δ shown; x is shown with the same number of digits to the right of the decimal point as is shown in δ.
  • In Around[x,δ], x and δ can be quantities with different, though compatible, units.
  • Around[{x1,x2,},δ] threads over the list in its first argument, effectively treating the uncertainties in the xi as being uncorrelated.

Examples

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Basic Examples  (10)

Uncertain numbers of different sizes and uncertainties:

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Uncertain Quantity objects with different units:

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An Around object with asymmetric uncertainties:

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Specify a 5% relative uncertainty in input:

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Perform operations with Around objects:

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Plot a list of Around objects:

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Extract the parts of an Around object:

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Two different instances of the same Around object are assumed to be uncorrelated:

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Therefore, the resulting uncertainty is smaller than that obtained by multiplication by 2:

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Use a symbolic Around object:

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Perform operations on it:

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Add symbolic Around objects, with uncertainties assumed to be uncorrelated:

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Scope  (14)

Applications  (3)

Properties & Relations  (1)

Introduced in 2019
(12.0)