How old (on average) is the human male when his body produces sperm
and he is able to ejaculate?

Some female teachers have been doing research in this area. I think in
some cultures males are married at 12.

Spermatogonia remain dormant until puberty.
(http://www.lab.anhb.uwa.edu.au/mb140/CorePages/MaleRepro/malerepro.htm)
and since males hit puberty between 10 and 14
(www.avert.org/puberty3.htm) this would be your answer.

Male Reproductive System. When boys reach puberty the pituitary gland
can start as early as age eight or nine or as late as age 15 or 16.
...

refer::
http://hes.ucf.k12.pa.us/gclaypo/repro/malerepr.html