Computing Variance manually problem

Question

Algorithms Analyst 2013-1-23

1
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https://ww2.mathworks.cn/matlabcentral/answers/59593-computing-variance-manually-problem

采纳的回答： Shashank Prasanna

HI all I am facing a problem in computing variance manualy.As

I have a A= magic(3) matrix of 9 elements

when I calculate it directly by using var it gives me

var(var(A)) ans is 27 but when I campute manually it does not match with above answer

As

variance=(A-mean(mean(A))).^2/8 variance=sum(sum(variance)) answer is 0. why is this situation occurring is there any problem in my formula?

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Answer 1

Shashank Prasanna 2013-1-23

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Your formula is wrong. when you say var(var(A)) you are actually computing the variances of each column and then variances of these variances. Is there a reason you are doing this? However if you are interested in reproducing the result, then you have to follow the same steps manually as follows:

 A = magic(3);
 B = sum((A-repmat(mean(A),3,1)).^2)/2; % Variance of each column
 var_magic = sum((B-mean(B)).^2)/2 % Variance of the variance computed above.
 var_magic =
      27