How to solve the problem that the demeaning of X gives a variable Y that has not exactly a zero mean, probably due to very small values ?

Question

Fox 2018-6-8

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https://ww2.mathworks.cn/matlabcentral/answers/404691-how-to-solve-the-problem-that-the-demeaning-of-x-gives-a-variable-y-that-has-not-exactly-a-zero-mean

回答： Sam Cook 2018-6-13

采纳的回答： Sam Cook

X.mat

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Hello together, I have the problem that I want to standardize a vector X. I do this by firstly demeaning X.

if true
  % Y=(X-mean(X))
end

However now I have the problem that the mean of Y is not exactly zero like it should be, but really close to zero like 1.8*e-18. I attached the values of X as a file here. If I only considereing the first 6 values of X its fine

Y=(X(1:6)-mean(X(1:6)),
mean(Y)=0

but if I include the really small value of X(7), I get this different result.

if true
  % Y=(X(1:7)-mean(X(1:7)),
mean(Y)=1.8e-10
end

Does anybody of you know what matlab is doing here? (rounding problem, too small number...)

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Answer 1

Sam Cook 2018-6-13

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https://ww2.mathworks.cn/matlabcentral/answers/404691-how-to-solve-the-problem-that-the-demeaning-of-x-gives-a-variable-y-that-has-not-exactly-a-zero-mean#answer_324541

This is a result of the accuracy of floating-point numbers. If you need to account for this, you can use the eps function to determine the degree of accuracy you are working with.