Mean or median absolute deviation
returns the
mean absolute deviation of the values in y
= mad(X
)X
.
If X
is a vector, then mad
returns the
mean or median absolute deviation of the values in X
.
If X
is a matrix, then mad
returns a row
vector containing the mean or median absolute deviation of each column of
X
.
If X
is a multidimensional array, then mad
operates along the first nonsingleton dimension of X
.
returns the mean or median absolute deviation over the dimensions specified in the vector
y
= mad(X
,flag
,vecdim
)vecdim
. For example, if X
is a 2-by-3-by-4 array,
then mad(X,0,[1 2])
returns a 1-by-1-by-4 array. Each element of the
output array is the mean absolute deviation of the elements on the corresponding page of
X
.
For normally distributed data, multiply mad
by one of the
following factors to obtain an estimate of the normal scale parameter
σ:
sigma = 1.253 * mad(X,0)
— For mean absolute
deviation
sigma = 1.4826 * mad(X,1)
— For median absolute
deviation
[1] Mosteller, F., and J. Tukey. Data Analysis and Regression. Upper Saddle River, NJ: Addison-Wesley, 1977.
[2] Sachs, L. Applied Statistics: A Handbook of Techniques. New York: Springer-Verlag, 1984, p. 253.