Mean
Mean[list]
gives the statistical mean of the elements in list.
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.
- Mean[list] is equivalent to Total[list]/Length[list].
- Mean handles both numerical and symbolic data.
- Mean[{{x1,y1,…},{x2,y2,…},…}] gives {Mean[{x1,x2,…}],Mean[{y1,y2,…}],…}.
- Mean[dist] is equivalent to Expectation[x,xdist].
Examples
open allclose allBasic Examples (4)
Scope (14)
Data (9)
Exact input yields exact output:
Approximate input yields approximate output:
Mean for a matrix gives columnwise means:
Mean for a tensor gives columnwise means at the first level:
SparseArray data can be used just like dense arrays:
Find the mean of WeightedData:
Find the mean of EventData:
Find the mean of a TimeSeries:
Distributions and Processes (5)
Find the mean for univariate distributions:
Mean for derived distributions:
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:
Applications (11)
The mean represents the center of mass for a distribution:
The mean for distributions without a single mode:
The mean for multivariate distributions:
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 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:
Compute the mean time to failure:
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:
Properties & Relations (15)
Mean is Total divided by Length:
Mean is equivalent to a 1‐norm divided by Length for positive values:
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 CentralMoment is the Mean of deviations raised to the n
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:
LocationEquivalenceTest tests for equivalence of means in two or more datasets:
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:
Text
Wolfram Research (2003), Mean, Wolfram Language function, https://reference.wolfram.com/language/ref/Mean.html (updated 2014).
CMS
Wolfram Language. 2003. "Mean." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2014. 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