"but why doesn't below work?"
Because you overwrite the results of every loop iteration with the results of the next iteration. Basically without indexing or some arithmetic you throw away the results of each loop iteration, except for the very last one. You need to do something like this:
function Z = mean2(vector)
N = numel(vector);
Z = 0;
for k = 1:N
Z = Z + vector(k)
end
Z = Z/N;
end
