# By element average of multiple matrices

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Bryan on 3 Apr 2012
Commented: Yash Ajay Garje on 18 Apr 2022
Hi,
I have 40 matrices of 781x981 in dimension. I need to calculate the by element mean of all these matrices in a new, 41st matrix.
I.e., the mean of element 1,1 of all 40 matrices is returned as element 1,1 in the new, 41st matrix. The same is then done for all elements.
In additionto the mean, I need to do the same for the standard deviation also.
Is there a function in Matlab that can do this? Or do I have to write some kind of a loop??
Thanks, Bryan

Wayne King on 3 Apr 2012
Yes, concatenate the matrices into a 3-D array and use mean(x,3)
x = randn(4,4,10);
mean(x,3)
and
std(x,[],3)
To concatenate, you can use cat()
x = randn(4,4);
y = randn(4,4);
z = cat(3,x,y);
mean(z,3)
std(z,[],3)
Jan on 3 Apr 2012
... and std(x, 0, 3);

### More Answers (1)

Sean de Wolski on 3 Apr 2012
Stack your 40 matrices into one three-dimensional matrix, then take the mean along the 3rd dimension
meanMatrix = mean(stackedMatrix,3); %doc mean for more info.
To stack your matrices look at these two FAQs:
Belinda Finlay on 17 Feb 2020
I am very new to MATLAB and am attempting a do a similar calacuation; however, I am having trouble stacking my matrices (as suggested by Sean), is someone able to guide me.
Thanks
Belinda
Yash Ajay Garje on 18 Apr 2022
Hi Belinda,
I do it like this:
A(:,:,1) = ['you could enter your 1st matrix here']
A(:,:,2) = ['you could enter your 2nd matrix here']
A(:,:,3) = ['you could enter your 3rd matrix here']
....
A(:,:,n) = ['you could enter your nth matrix here']
As a result, you would have created a matrix 'A' with the third dimension as 'n'. You could also loop this if required. Hope this helps.
Best,
Yash