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.
  • The singular case MeanAround[{x}] is defined to return x with zero uncertainty.

Examples

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Basic Examples  (5)

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

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

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

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

MeanAround on a list of vectors returns a VectorAround object:

Scope  (4)

Scalar Mean with Uncertainty  (3)

Compute the mean Around object for a list of numbers:

Compute the mean Around object for a list of energies:

Find the weighted mean of a list of Around objects:

Compare to the result of MeanAround on the bare values, ignoring the original uncertainties:

Compare with a direct mean on the original list:

Vector Mean with Uncertainty  (1)

Compute the mean of a list of {length,time} pairs:

Applications  (1)

Download 100 random movie entities and find their runtimes:

There is a wide distribution of runtime values:

These are the mean value and the standard deviation of runtimes:

This is the mean with its uncertainty:

Properties & Relations  (2)

Take a normal distribution and simulate it:

Around[scalars] estimates the mean and standard deviations of the distribution:

Around[dist] gives the true parameters in the distribution dist:

MeanAround[scalars] describes the mean of the distribution and the standard error of the mean:

Take a multinormal distribution for 2D vectors and simulate it:

VectorAround[vectors] estimates the mean and covariance matrices of the distribution:

MeanAround[scalars] describes the mean of the distribution and the covariance matrix associated with that mean:

Wolfram Research (2019), MeanAround, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanAround.html.

Text

Wolfram Research (2019), MeanAround, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanAround.html.

CMS

Wolfram Language. 2019. "MeanAround." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeanAround.html.

APA

Wolfram Language. (2019). MeanAround. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanAround.html

BibTeX

@misc{reference.wolfram_2024_meanaround, author="Wolfram Research", title="{MeanAround}", year="2019", howpublished="\url{https://reference.wolfram.com/language/ref/MeanAround.html}", note=[Accessed: 26-December-2024 ]}

BibLaTeX

@online{reference.wolfram_2024_meanaround, organization={Wolfram Research}, title={MeanAround}, year={2019}, url={https://reference.wolfram.com/language/ref/MeanAround.html}, note=[Accessed: 26-December-2024 ]}