MeanDeviation
MeanDeviation[list]
gives the mean absolute deviation from the mean of the elements in list.
Details

- For the list {x1,x2,…,xn}, the mean deviation is given by
, where
is the mean of the list.
- MeanDeviation handles both numerical and symbolic data.
- MeanDeviation[{{x1,y1,…},{x2,y2,…},…}] gives {MeanDeviation[{x1,x2,…}],MeanDeviation[{y1,y2,…},…]}.
Examples
open allclose allBasic Examples (2)
Scope (9)
Exact input yields exact output:
Approximate input yields approximate output:
MeanDeviation for a matrix gives columnwise means:
SparseArray data can be used just like dense arrays:
Find the mean deviation of WeightedData:
Find the mean deviation of EventData:
Find the mean deviation for TimeSeries:
Generalizations & Extensions (1)
Compute results for a SparseArray:
Applications (3)
Properties & Relations (4)
MeanDeviation is the Mean of absolute deviations from the Mean:
MeanDeviation is equivalent to the 1‐norm of the deviations divided by the Length:
For large uniform datasets, MeanDeviation and MedianDeviation are nearly the same:
MeanDeviation as a scaled ManhattanDistance from the Mean:
Neat Examples (1)
Ratio of MeanDeviation to MedianDeviation for increasing sample size:
Text
Wolfram Research (2007), MeanDeviation, Wolfram Language function, https://reference.wolfram.com/language/ref/MeanDeviation.html.
CMS
Wolfram Language. 2007. "MeanDeviation." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MeanDeviation.html.
APA
Wolfram Language. (2007). MeanDeviation. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MeanDeviation.html