As some one who has always lived in Leeds, crime threads about it really suprise me!! But yes I am aware everyone's experience is different!
Daytime city centre- I often go on my own, shopping ect, never ever feel intimidated or have seen any crime.
Nightime city centre- Often go clubbing with jus one or two other girls (we are all 18) and again, never had any bad experiences. Generally at about 3 in the morning we walk from one end of town to the other to get a taxi from train station (as do many people) and even then there is no fear of anything at all, just friendly drunken boys really!
Of course there are areas to avoid, like harehills and chapletown, but you would never have to go there!
Now headingly is where most students live (just outside city centre) and of course you might get broken in to, just like anywhere else! But if your wondering how safe it is at night there is no need. Many young people, certainly not just the uni students, are more recently going with the trend of going to headingly on a night out instead of the city centre, and they wouldnt do that if they didnt feel safe.
But, clearly I can understand the concerns of the crime statistics, I myself might be going to Nottingham and obviously am all "oh my god, I might get shot"!!