Finding the Sample Mean of a Matrix

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SUMMARY

The discussion centers on calculating the sample mean of a matrix, specifically addressing the interpretation of "sample mean" in this context. It is established that if the entries of the matrix represent samples, the mean can be calculated as the average of the largest and smallest values in an arithmetic series. For the matrix entries "1, 2, 3, ... 14, 15, 16," the sample mean is determined to be 8.5. Additionally, if each column or row represents different samples, the sample mean would be the row matrix of the column means, necessitating further context for accurate interpretation.

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EnglsihLearner
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What is the sample mean of the following matrix?

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I'm afraid you are going to have to define "sample mean" for a matrix. I have never seen that term before. I suspect that the entries in the matrix are "samples" of some kind but you did not say that.

IF the entries are the "samples" and you are asking for the mean of these numbers then "1, 2, 3, ... 14, 15, 16" are an arithmetic series and the mean of such a series is just the mean of largest and smallest values. That is (1+ 2+ 3+ ...+ 15+ 16)/16= (1+ 16)/2= 17/2.
 
If each column represents a different (small) sample the sample mean would be the row matrix of column means. A similar comment would apply if each row is a sample.
If neither of those descriptions apply then more context is needed.

Is this from a multivariate problem?
 

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