Mean value(centroid) of a collection of vectors

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If I have a collection of vectors in very high euclidean space(n=72). How do I find the mean value of all the vectors? Maybe I'm using the incorrect terminology. Maybe I want to find the centroid of where all these vectors are?? I'm working on a machine learning algorithm. Any help would be greatly appreciated.
 
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I'm essentially looking a for a vector that would give a good indication of where all the other vectors are clustered together. I hope to add new vectors to this group based on cosine similarity of the new vector and the mean value.
 

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