Stonger EN means weaker bases and weaker EN mean stronder basicity WITHIN A GROUP.
Going down a group, generally EN decreases and atoms get bigger. Increase in size means greater polarizabilty. Both factors increase leaving group ability. In general halogens are good LG groups and LG ability increases down the group.
I hope this helps.
I disagree with this. Lower electronegativity does not enhance leaving group ability. In fact, it diminishes leaving group ability. However, when you're going down a group of the periodic table, size of the electron cloud, and thus polarizability, is much much more important because atomic radius increases drastically for each step down the table. When you go across a row, there is little difference in polarizability, and a much bigger difference in electronegativity, so electronegativity drives acidity/basicity and leaving group ability across rows.
All halides except for fluoride are very very very weak bases (of the common ones, I- is the weakest) because they stabilize their negative charge very well due to high polarizability. This is related to leaving group ability because leaving group ability depends on the stability of the leaving group once it has accepted an electron pair (in other words, it depends on the stability of the leaving group once it has "left"). Thus, a leaving group that is a weaker base (more able to stabilize a negative charge) will also be a better leaving group.
So as Bernoull said, leaving group ability increases as you go down the periodic table. However, fluoride is an extremely poor leaving group and will, in general, never act as a leaving group (there are exceptions, but not many). Fluoride is a weak base (the pKa of HF is 3.2, versus -7 for HCl, -9 for HBr, and -10 for HI), but it is a 10^10 fold stronger base than chloride, so I think it is clear why fluoride is not a good leaving group.