What is the sample mean of the following matrix?
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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