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Variance, ignoring NaN values


y = nanvar(X)
y = nanvar(X,w)
y = nanvar(X,w,'all')
y = nanvar(X,w,dim)
y = nanvar(X,w,vecdim)



y = nanvar(X) is the variance var of X, computed after removing NaN values.

For vectors x, nanvar(x) is the sample variance of the remaining elements, once NaN values are removed. For matrices X, nanvar(X) is a row vector of column sample variances, once NaN values are removed. For multidimensional arrays X, nanvar operates along the first nonsingleton dimension.

nanvar removes the mean from each variable (column for matrix X) before calculating y. If n is the number of remaining observations after removing observations with NaN values, nanvar normalizes y by either n – 1 or n, depending on whether n > 1 or n = 1, respectively.

y = nanvar(X,w) computes the variance of X according to the weighting scheme w. When w is 0 (default), X is normalized by n – 1, where n is the number of non-NaN observations. When w is 1, w is normalized by the number of non-NaN observations. Otherwise, w can be a weight vector containing nonnegative elements. The length of w must equal the length of the dimension over which nanvar operates. Elements of X corresponding to NaN values of w are ignored.

y = nanvar(X,w,'all') returns the variance over all elements of X when w = 0 or w = 1. The nanvar function computes the variance after removing NaN values.

y = nanvar(X,w,dim) returns the variance along the operating dimension dim of X.


y = nanvar(X,w,vecdim) returns the variance over the dimensions specified in the vector vecdim, computed after removing NaN values. Each element of vecdim represents a dimension of the input array X. The output y has length 1 in the specified operating dimensions. The other dimension lengths are the same for X and y. For example, if X is a 2-by-3-by-4 array, then nanvar(X,[],[1 2]) returns a 1-by-1-by-4 array. Each element of the output array is the variance of the elements on the corresponding page of X. This syntax is supported when w = 0 or w = 1.


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Find the column variances for matrix data with missing values.

X = magic(3);
X([1 6:9]) = NaN
X = 3×3

   NaN     1   NaN
     3     5   NaN
     4   NaN   NaN

y = nanvar(X)
y = 1×3

    0.5000    8.0000       NaN

Find the variance of a multidimensional array over multiple dimensions.

Create a 3-by-4-by-2 array X with some missing values.

X = reshape(1:24,[3 4 2]);
X([8:10 18]) = NaN
X = 
X(:,:,1) =

     1     4     7   NaN
     2     5   NaN    11
     3     6   NaN    12

X(:,:,2) =

    13    16    19    22
    14    17    20    23
    15   NaN    21    24

Find the sample variance of each page of X by specifying dimensions 1 and 2 as the operating dimensions.

ypage = nanvar(X,0,[1 2])
ypage = 
ypage(:,:,1) =


ypage(:,:,2) =


For example, ypage(1,1,2) is the sample variance of the non-NaN elements in X(:,:,2).

Find the sample variance of the elements in each X(:,i,:) slice by specifying dimensions 1 and 3 as the operating dimensions.

ycol = nanvar(X,0,[1 3])
ycol = 1×4

   44.0000   40.3000   42.9167   40.3000

For example, ycol(4) is the sample variance of the non-NaN elements in X(:,4,:).

Alternative Functionality

Instead of using nanvar, you can use the MATLAB® function var with the input argument nanflag specified as the value 'omitnan'.

Extended Capabilities

See Also

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Introduced before R2006a