What I've been told is that for most guys it grows a lot between 13 and 14. There was one month where I think mine grew like a quarter inch. I'm not sure knowing the average size is all that helpful because so much depends on where you are in puberty. If you just started puberty it will be small yeah but it will change big time soon. If you started puberty early then it's probably big already but won't grow much more. Just sayin that things change so fast at our age that knowing what is average might not help much if you are wondering how big you will be when you grow up. I'd say maybe just look around a bit in P.E. showers and as long as you aren't the biggest or the smallest than you're probably pretty average.
There are not many statistics covered for every age, and those that do get quoted are probably not very reliable. Some guys are already well into puberty at 13, others may not even have started, so pretty much any penis size is normal.