# 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)

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: