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Mean—Wolfram Language Documentation

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• See Also
  • TrimmedMean
  • WinsorizedMean
  • Median
  • BiweightLocation
  • GeometricMean
  • HarmonicMean
  • ContraharmonicMean
  • MeanFilter
  • MeanAround
  • Midpoint
  • Total
  • StandardDeviation
  • Variance
  • RootMeanSquare
  • MeanDeviation
  • Standardize
  • Rescale
  • Commonest
  • Expectation
• Related Guides
  • Descriptive Statistics
  • Random Processes
  • GPU Computing
  • Time Series Processing
  • Reliability
  • Arithmetic Functions
  • Spatial Point Collections
  • GPU Computing with NVIDIA
  • GPU Computing with Apple
  • Tabular Processing Overview
  • Statistical Data Analysis
  • Tabular Modeling
  • Probability & Statistics with Quantities
  • Precollege Education
  • Computation with Structured Datasets
  • Math & Counting Operations on Lists
  • Date & Time
  • Numerical Data
  • Scientific Data Analysis
  • Statistical Moments and Generating Functions
  • Discrete & Integer Data
  • Image Processing & Analysis
  • Numbers with Uncertainty
  • Spatial Statistics
  • Using the Wolfram Data Drop
  • Probability & Statistics
  • Tabular Transformation
  • Signal Visualization & Analysis
  • Survival Analysis
  • Audio Processing
  • Symbolic Vectors, Matrices and Arrays
  • GPU Programming
• Tech Notes
  • Basic Statistics
  • Descriptive Statistics
  • Discrete Distributions
  • Continuous Distributions

Mean[data]

gives the mean estimate of the elements in data.

Mean[dist]

gives the mean of the distribution dist.

• 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:
• 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,xdist]. »
• For multivariate distribution dist, the mean is given by {μ_x ,μ_y,…}=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]]. »

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:

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:

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:

Channel-wise mean value of an RGB image:

Mean intensity value of a grayscale image:

On audio objects, Mean works channel-wise:

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:

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:

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:

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:

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:

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

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