gives the median estimate of the elements in data.


gives the median of the distribution dist.



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Basic Examples  (3)

Find the middle value in the list:

Average the two middle values:

Median of a parametric distribution:

Scope  (19)

Basic Uses  (8)

Exact input yields exact output:

Approximate input yields approximate output:

Find the median of WeightedData:

Find the median of EventData:

Find the median of TemporalData:

Find the median of a TimeSeries:

The median depends only on the values:

Find a three-element moving median:

Find the median of data involving quantities:

Array Data  (5)

Median for a matrix gives columnwise medians:

Median for a tensor gives columnwise medians at the first level:

Works with large arrays:

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

SparseArray data can be used just like dense arrays:

Find median of a QuantityArray:

Image and Audio Data  (2)

Channel-wise median value of an RGB image:

Median intensity value of a grayscale image:

Median amplitude of all amplitude values of all channels:

Distributions and Processes  (4)

Find the median for a parametric distribution:

Median for a derived distribution:

Data distribution:

Median for distributions with quantities:

Median function for a time slice of a random process:

Applications  (7)

The median represents the center of a distribution:

The median for a distribution without a single mode:

Find the median length, in miles, for 141 major rivers in North America:

Plot a Histogram for the data:

Probability that the length exceeds 90% of the median:

Smooth an irregularly spaced time series using a moving median:

A 90-day moving median:

Obtain a robust estimate of location when outliers are present:

Extreme values have a large influence on the Mean:

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

Choose a few slice times:

Plot medians over these paths:

Find the median height for the children in a class:

Properties & Relations  (7)

Median is equivalent to a parametrized Quantile:

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

For univariate data, Median coincides with SpatialMedian:

The Median of absolute deviations from the Median is MedianDeviation:

MovingMedian is a sequence of medians:

For any distribution, there is InverseCDF[dist,1/2]=Median[dist]:

Similarly for InverseSurvivalFunction:

For a continuous distribution, there is CDF[dist,Median[dist]]=1/2:

Similarly for SurvivalFunction:

For discrete distributions, the identity does not hold:

Possible Issues  (2)

Median requires numeric values:

Median of data computed via Quantile does not always agree with Median:

Calculate median directly:

Specify linear interpolation parameters in Quantile:

Neat Examples  (1)

The distribution of Median estimates for 20, 100, and 300 samples:

Wolfram Research (2003), Median, Wolfram Language function, (updated 2023).


Wolfram Research (2003), Median, Wolfram Language function, (updated 2023).


Wolfram Language. 2003. "Median." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023.


Wolfram Language. (2003). Median. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_median, author="Wolfram Research", title="{Median}", year="2023", howpublished="\url{}", note=[Accessed: 20-July-2024 ]}


@online{reference.wolfram_2024_median, organization={Wolfram Research}, title={Median}, year={2023}, url={}, note=[Accessed: 20-July-2024 ]}