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Mean

Mean[data]

gives the mean estimate of the elements in data.

Mean[dist]

gives the mean of the distribution dist.

Details
Details and Options Details and Options
Examples  
Basic Examples  
Scope  
Basic Uses  
Array Data  
Image and Audio Data  
Date and Time  
Distributions and Processes  
Applications  
Basic Applications  
Applications  
Properties & Relations  
Possible Issues  
Neat Examples  
See Also
Tech Notes
Related Guides
History
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Mean

Mean[data]

gives the mean estimate of the elements in data.

Mean[dist]

gives the mean of the distribution dist.

Details

  • Mean is also known as an expectation or average.
  • Mean is a location measure for data or distributions.
  • For VectorQ data , the mean estimate is given by .
  • For MatrixQ data, the mean estimate is computed for each column vector with Mean[{{x1,y1,…},{x2,y2,…},…}] equivalent to {Mean[{x1,x2,…}],Mean[{y1,y2,…}],…}. »
  • For ArrayQ data, the mean estimate is equivalent to ArrayReduce[Mean,data,1]. »
  • For WeightedData[{x1,x2,…},{w1,w2,…}], the mean estimate is given by . »
  • Mean handles both numerical and symbolic data.
  • The data can have the following additional forms and interpretations:
  • Associationthe values (the keys are ignored) »
    WeightedDataweighted mean, based on the underlying EmpiricalDistribution »
    EventDatabased on the underlying SurvivalDistribution »
    TimeSeries, TemporalData, …vector or array of values (the time stamps ignored) »
    Image,Image3DRGB channels values or grayscale intensity value »
    Audioamplitude values of all channels »
    DateObject,TimeObjectlist of dates or list of times »
  • For a list of dates , the mean is given by , which is date plus sum of durations .
  • For a univariate distribution dist, the mean is given by μ=Expectation[x,xdist]. »
  • For multivariate distribution dist, the mean is given by {μx ,μy,…}=Expectation[{x,y,…},{x,y,…}dist]. »
  • For a random process proc, the mean function can be computed for slice distribution at time t, SliceDistribution[proc,t], as μ[t]=Mean[SliceDistribution[proc,t]]. »

Examples

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Basic Examples  (5)

Mean of numeric values:

Mean of symbolic values:

Means of elements in each column:

Mean of a list of dates:

Mean of a parametric distribution:

Scope  (22)

Basic Uses  (6)

Exact input yields exact output:

Approximate input yields approximate output:

Find the mean of WeightedData:

Find the mean of EventData:

Find the mean of a TimeSeries:

The mean depends only on the values:

Compute a weighted mean:

Find the mean of data involving quantities:

Array Data  (5)

Mean for a matrix gives columnwise means:

Mean for a arrays gives columnwise means at the first level:

Works with large arrays:

When the input is an Association, Mean works on its values:

SparseArray data can be used just like dense arrays:

Find mean of a QuantityArray:

Image and Audio Data  (2)

Channel-wise mean value of an RGB image:

Mean intensity value of a grayscale image:

On audio objects, Mean works channel-wise:

Date and Time  (4)

Compute mean of dates:

Compute the weighted mean of dates:

Compute the mean of dates given in different calendars:

The mean is given in one of the input calendars:

Compute the mean of times:

List of times with different time zone specifications:

Distributions and Processes  (5)

Find the mean for univariate distributions:

Multivariate distributions:

Mean for derived distributions:

Data distribution:

Mean for distributions with quantities:

Mean function for a continuous-time random and discrete-state process:

Find the mean of TemporalData at some time t=0.5:

Find the mean function together with all the simulations:

Applications  (11)

Basic Applications  (5)

The mean represents the center of mass for a distribution:

The mean for distributions without a single mode:

The mean for multivariate distributions:

Mean values of cells in a sequence of steps of 2D cellular automaton evolution:

Compute means for slices of a collection of paths of a random process:

Choose a few slice times:

Plot means over these paths:

Applications  (6)

Find the mean height for the children in a class:

Find the mean height for the children in a class:

Find the mean strength for 480 samples of ceramic material:

Plot a Histogram for the data with mean position highlighted:

Compute the probability that the strength exceeds the mean:

Compute the mean lifetime for a quantity subject to exponential decay with rate :

Smooth an irregularly spaced time series by computing a moving mean:

A 90-day moving mean:

A vacuum system in a small electron accelerator contains 20 vacuum bulbs arranged in a circle. The vacuum system fails if at least 3 adjacent vacuum bulbs fail:

Plot the survival function:

Compute the mean time to failure:

Properties & Relations  (17)

Mean is Total divided by Length:

Mean is equivalent to a 1‐norm divided by Length for positive values:

Mean of WeightedData is equivalent to the mean of the EmpiricalDistribution of the data:

Mean of EventData is equivalent to the mean of the SurvivalDistribution of the data:

For nearly symmetric samples, Mean and Median are nearly the same:

The Mean of absolute deviations from the Mean is MeanDeviation:

Mean is logarithmically related to GeometricMean for positive values:

Mean is the inverse of HarmonicMean of the inverse of the data:

The square root of Mean of the data squared is RootMeanSquare:

The n^(th) CentralMoment is the Mean of deviations raised to the n^(th) power:

Variance is a scaled Mean of squared deviations from the Mean:

Expectation for a list is a Mean:

MovingAverage is a sequence of means:

A 0% TrimmedMean is the same as Mean:

The Expectation of a random variable in a distribution is the Mean:

LocationTest tests whether the mean is close to 0:

The probability () value:

LocationEquivalenceTest tests for equivalence of means in two or more datasets:

The probability () value:

Possible Issues  (1)

Outliers can have a disproportionate effect on Mean:

Use TrimmedMean to ignore a fraction of the smallest and largest elements:

Use Median as something much less sensitive to outliers:

Neat Examples  (1)

The distribution of Mean estimates for 10, 100, and 300 samples:

Wolfram Research (2003), Mean, Wolfram Language function, https://reference.wolfram.com/language/ref/Mean.html (updated 2024).

Text

Wolfram Research (2003), Mean, Wolfram Language function, https://reference.wolfram.com/language/ref/Mean.html (updated 2024).

CMS

Wolfram Language. 2003. "Mean." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2024. https://reference.wolfram.com/language/ref/Mean.html.

APA

Wolfram Language. (2003). Mean. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Mean.html

BibTeX

@misc{reference.wolfram_2025_mean, author="Wolfram Research", title="{Mean}", year="2024", howpublished="\url{https://reference.wolfram.com/language/ref/Mean.html}", note=[Accessed: 01-December-2025]}

BibLaTeX

@online{reference.wolfram_2025_mean, organization={Wolfram Research}, title={Mean}, year={2024}, url={https://reference.wolfram.com/language/ref/Mean.html}, note=[Accessed: 01-December-2025]}