MeanAround

MeanAround[{x1,x2,x3,}]

gives an Around object describing the mean of the xi and its uncertainty.

MeanAround[{{x11,x12,},{x21,},}]

gives a VectorAround object describing the means of the vectors xi and their covariance.

Details • The objects xi can be numbers, quantities or Around objects.
• MeanAround[{Around[x1,δ1],}] computes the weighted mean of the xi, with weights proportional to 1/δi2.
• For a list of n numbers or quantities, MeanAround[list] gives Around[Mean[list], ].
• For a list of n vectors, MeanAround[list] gives VectorAround[Mean[list], ].
• In MeanAround[{{x11,x12,},{x21,x22,},}], the xij can be quantities, so long as the units of all x1j, all x2j, etc. are compatible.

Examples

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Basic Examples(5)

Find the mean of a list of numbers, tagged with its uncertainty:

 In:= Out= In:= Out= In:= Out= Find the mean of a list of Quantity objects, tagged with its uncertainty:

 In:= In:= Out= In:= Out= Find the mean of a simulation of a normal distribution centered at 3:

 In:= Out= In:= Out= If the simulation contains many more points, the uncertainty of the mean is lower:

 In:= In:= Out= MeanAround on a list of vectors returns a VectorAround object:

 In:= Out= In:= Out= Applications(1)

Introduced in 2019
(12.0)