I learnt Fur Elise when I was 9. I was about Grade 5 at the time, but I did skip Grade 4. I managed to memorise it, and I mean the whole 5 page one. I played it at a school residential since there was a piano, and everyone wanted me too. In my end-of-year school report, my teacher had written "it was a genuinely moving performance".
I perform in a lot of public concerts. It's usually the Chinese Community ones that my teacher is involved in and all of the students prepare something and play. Please note that the youngest of these students is 4 years old and beginner standard. But everyone still applauds and enjoys their performance! Whereas I myself and other people play much higher standard Grade 6+ stuff, with emotion, hopefully