MATLAB: Finding the standard deviation for every single value in a matrix

deviationMATLABmean

Hi Everyone,

I have a 10 matrices X1, X2,X3……X10. Each matrix has a size of (512×30).

1- i want to calculate the mean for all , and the output matrix must be in the same size as input (512×30).

2- Then, i want to calculate the standard deviation for all , and the output matrix must be in the same size as input (512×30).

Any help will be apperciated.

Best Answer

X=cat(3, X1,X2,X3,X4,X5,X6,X7,X8,X9,X10); %It was a mistake to create 10 separate matrices.
MeansX=mean(X,3),
StdX = std(X,[],3)

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MATLAB: How to use for loop to reduce the number of lines from the following code

This is MATLAB, so here is a much simpler solution without any loops:

M  = C1(1:399,5:11);
R  = mean(permute(M,[3,2,1]).*permute(M,[2,3,1]),3);
R0 = mean(M.*C1(1:399,13),1).';
B  = pinv(R)*(R0)

And compared against the output of your code:

>> isequal(A,B)
ans = 1

For MATLAB versions prior to R2016b you will need replace the .* operators with bsxfun and times.

MATLAB: Standard deviation of values with standard deviation

The question you are asking is a specific instance of "propagation of uncertainty". You might want to learn more about the topic.

For this specific case, I believe the answer is

std_sum = sqrt(1^2 + 2^2 + 3^2); % error of sum = square root of (sum of squares of individual uncertainties)
std_mean = std_sum/3
std_mean = 1.2472

Here is a simulation that suggests that this is correct:

rng default
N = 100000;
x1 = 10 + 1*randn(N,1);
x2 = 15 + 2*randn(N,1);
x3 = 20 + 3*randn(N,1);
x = [x1, x2, x3];
mean_x = mean(x,2);
mean(mean_x)
ans = 15.0007
std(mean_x,1)
ans = 1.2459
figure
subplot(4,1,1), histogram(x(:,1))
xlim([0 30])
subplot(4,1,2), histogram(x(:,2))
xlim([0 30])
subplot(4,1,3), histogram(x(:,3))
xlim([0 30])
subplot(4,1,4), histogram(mean_x)
xlim([0 30])

I would encourage you to be really careful about your terminology. Often when people write x +/- dx, dx refers to the standard error, not the standard deviation. The standard deviation is a property of the parent population. The standard error (of the mean, for example) will depend on the sampling -- specifically on sample size.

I think that what I have written above probably corresponds to what you wanted to know, but be careful.

Best Answer

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